Solving 800-90 Entropy Requirements in Software

23
Solving the Challenge of New Entropy Standards Ray Potter ICMC November 20, 2014

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Transcript of Solving 800-90 Entropy Requirements in Software

Page 1: Solving 800-90 Entropy Requirements in Software

Solving the Challenge of New Entropy Standards

Ray Potter

ICMC

November 20 2014

Flow

bull Quick recap of entropy and its purpose

bull Standards reviewbull Our work

Entropy

bull Average amount of information contained in data stream

bull A measure of uncertainty unpredictability

Practical Entropy

S a f L og i c

Ru l s

Entropy in the Real World

Entropy in Crypto

bull Provide random bitsbull Challenges in authentication

protocolsbull Seeds for algorithmsbull Use to seed DRBG

bull Value is unpredictable output

Issues

bull Truly random data difficult impossible to generate on a computer

bull How to measure it

Entropy Quantified

bull log2 (max p(xi)) bull minus1113090 P(X = x)log P(X = x)

NIST 800 Series

bull SP 800-90B requirements for entropy source

bull SP 800-90A deterministic algorithms bull SP 800-90C implement an RBG with -

90A and -90B components

Effect to FIPS 140

bull Current Requirement

ldquoCompromising the security of the key generation method (eg guessing the seed value to initialize the deterministic RNG) shall require as least as many operations as determining the value of the generated keyrdquo

Draft IG

bull First socialized last yearbull Entropy estimation mandatory forhellip

software modules which include entropy gathering mechanisms that are within the logical boundary of the module

Entropy Gathered within SW Module Logical Boundary

bull CMTL needs to submit entropy rationale

bull If DRBG is reseeded frequently the vendor shall make a reasonable heuristic claim of independence of the added entropy values

Entropy Gathered Outside the SW Module Logical

Boundarybull Entropy estimate should be in SP

1Entropy originates from another validated module

2Entropy originates from the operational environment

ChaosControl

bull Cryptographically secure DRBG

bull Available for mobile and desktop server environments

bull Compliant to 800-90 and draft FIPS 140 IG

Logical View of Entropy Sources for iOS Platform

Words from Whit

bull The right way to use tests in random number generation is to look for failure of the particular mechanism

bull Test each source independently (for stuck faults and other things that can be detected by correlation) and shut down if fewer than some threshold pass the test

Checks Performed

bull Entropy estimates for each source is recorded with that source

bull Exception reinitialize if not enough entropy

bull CRNGT (CREGT)

Initial Seeding

bull Ensures sufficient entropy before allowing clients to request random bytes

bull Checks for suitable amount of entropy before initialization

bull Seed file is persisted to disk

More about Tests

bull Heuristic bull log2 (max p(xi)) min-entropy from

800-90bbull Statistical Tests from 800-90bbull Full test suite documented by NIST

SP800-22rev1a

Results from 800-22rev1a

Statistical Analysis Results

Compression Bins CollisionOutput Space Size = 256Minimum Possible Score 0000000Maximum Possible Score 7183666Filename outbinTest name compressionOutput Space Size 256Number of samples 58321Number of events 57321Mean score 7139077Adjusted mean score 7126542Standard deviation 1818899Entropy type min-entropyEntropy estimate 4936194Entropyoutputdimension estimate 0617024

Output Space Size = 256Warning Shannon entropy estimate = 797Filename outbinTest name binsOutput Space Size 256Number of samples 58321Number of events 58321Mean score 0006927Adjusted mean score 0015471Standard deviation 0000000Entropy type min-entropyEntropy estimate 6014244Entropyoutputdimension estimate 0751781

Output Space Size = 256Minimum Possible Score 2000000Maximum Possible Score 20726106Filename outbinTest name collisionOutput Space Size 256Number of samples 58313Number of events 2803Mean score 20803782Adjusted mean score 20493429Standard deviation 9956489Entropy type min-entropyEntropy estimate 6103266Entropyoutputdimension estimate 0762908

Hey Guess Whathellip

bull ChaosControl is included with CryptoComply

bull ChaosControl is (nearly) patented

bull SafeLogic is offering it standalone at NO COST license until the end of Q1CY2015

Letrsquos Connect

bull SafeLogic

bull SafeLogic_Ray

bull wwwSafeLogiccom

  • Solving the Challenge of New Entropy Standards
  • Flow
  • Entropy
  • Practical Entropy
  • Entropy in the Real World
  • Entropy in Crypto
  • Issues
  • Entropy Quantified
  • NIST 800 Series
  • Effect to FIPS 140
  • Draft IG
  • Entropy Gathered within SW Module Logical Boundary
  • Entropy Gathered Outside the SW Module Logical Boundary
  • ChaosControl
  • Logical View of Entropy Sources for iOS Platform
  • Words from Whit
  • Checks Performed
  • Initial Seeding
  • More about Tests
  • Results from 800-22rev1a
  • Statistical Analysis Results
  • Hey Guess Whathellip
  • Letrsquos Connect
Page 2: Solving 800-90 Entropy Requirements in Software

Flow

bull Quick recap of entropy and its purpose

bull Standards reviewbull Our work

Entropy

bull Average amount of information contained in data stream

bull A measure of uncertainty unpredictability

Practical Entropy

S a f L og i c

Ru l s

Entropy in the Real World

Entropy in Crypto

bull Provide random bitsbull Challenges in authentication

protocolsbull Seeds for algorithmsbull Use to seed DRBG

bull Value is unpredictable output

Issues

bull Truly random data difficult impossible to generate on a computer

bull How to measure it

Entropy Quantified

bull log2 (max p(xi)) bull minus1113090 P(X = x)log P(X = x)

NIST 800 Series

bull SP 800-90B requirements for entropy source

bull SP 800-90A deterministic algorithms bull SP 800-90C implement an RBG with -

90A and -90B components

Effect to FIPS 140

bull Current Requirement

ldquoCompromising the security of the key generation method (eg guessing the seed value to initialize the deterministic RNG) shall require as least as many operations as determining the value of the generated keyrdquo

Draft IG

bull First socialized last yearbull Entropy estimation mandatory forhellip

software modules which include entropy gathering mechanisms that are within the logical boundary of the module

Entropy Gathered within SW Module Logical Boundary

bull CMTL needs to submit entropy rationale

bull If DRBG is reseeded frequently the vendor shall make a reasonable heuristic claim of independence of the added entropy values

Entropy Gathered Outside the SW Module Logical

Boundarybull Entropy estimate should be in SP

1Entropy originates from another validated module

2Entropy originates from the operational environment

ChaosControl

bull Cryptographically secure DRBG

bull Available for mobile and desktop server environments

bull Compliant to 800-90 and draft FIPS 140 IG

Logical View of Entropy Sources for iOS Platform

Words from Whit

bull The right way to use tests in random number generation is to look for failure of the particular mechanism

bull Test each source independently (for stuck faults and other things that can be detected by correlation) and shut down if fewer than some threshold pass the test

Checks Performed

bull Entropy estimates for each source is recorded with that source

bull Exception reinitialize if not enough entropy

bull CRNGT (CREGT)

Initial Seeding

bull Ensures sufficient entropy before allowing clients to request random bytes

bull Checks for suitable amount of entropy before initialization

bull Seed file is persisted to disk

More about Tests

bull Heuristic bull log2 (max p(xi)) min-entropy from

800-90bbull Statistical Tests from 800-90bbull Full test suite documented by NIST

SP800-22rev1a

Results from 800-22rev1a

Statistical Analysis Results

Compression Bins CollisionOutput Space Size = 256Minimum Possible Score 0000000Maximum Possible Score 7183666Filename outbinTest name compressionOutput Space Size 256Number of samples 58321Number of events 57321Mean score 7139077Adjusted mean score 7126542Standard deviation 1818899Entropy type min-entropyEntropy estimate 4936194Entropyoutputdimension estimate 0617024

Output Space Size = 256Warning Shannon entropy estimate = 797Filename outbinTest name binsOutput Space Size 256Number of samples 58321Number of events 58321Mean score 0006927Adjusted mean score 0015471Standard deviation 0000000Entropy type min-entropyEntropy estimate 6014244Entropyoutputdimension estimate 0751781

Output Space Size = 256Minimum Possible Score 2000000Maximum Possible Score 20726106Filename outbinTest name collisionOutput Space Size 256Number of samples 58313Number of events 2803Mean score 20803782Adjusted mean score 20493429Standard deviation 9956489Entropy type min-entropyEntropy estimate 6103266Entropyoutputdimension estimate 0762908

Hey Guess Whathellip

bull ChaosControl is included with CryptoComply

bull ChaosControl is (nearly) patented

bull SafeLogic is offering it standalone at NO COST license until the end of Q1CY2015

Letrsquos Connect

bull SafeLogic

bull SafeLogic_Ray

bull wwwSafeLogiccom

  • Solving the Challenge of New Entropy Standards
  • Flow
  • Entropy
  • Practical Entropy
  • Entropy in the Real World
  • Entropy in Crypto
  • Issues
  • Entropy Quantified
  • NIST 800 Series
  • Effect to FIPS 140
  • Draft IG
  • Entropy Gathered within SW Module Logical Boundary
  • Entropy Gathered Outside the SW Module Logical Boundary
  • ChaosControl
  • Logical View of Entropy Sources for iOS Platform
  • Words from Whit
  • Checks Performed
  • Initial Seeding
  • More about Tests
  • Results from 800-22rev1a
  • Statistical Analysis Results
  • Hey Guess Whathellip
  • Letrsquos Connect
Page 3: Solving 800-90 Entropy Requirements in Software

Entropy

bull Average amount of information contained in data stream

bull A measure of uncertainty unpredictability

Practical Entropy

S a f L og i c

Ru l s

Entropy in the Real World

Entropy in Crypto

bull Provide random bitsbull Challenges in authentication

protocolsbull Seeds for algorithmsbull Use to seed DRBG

bull Value is unpredictable output

Issues

bull Truly random data difficult impossible to generate on a computer

bull How to measure it

Entropy Quantified

bull log2 (max p(xi)) bull minus1113090 P(X = x)log P(X = x)

NIST 800 Series

bull SP 800-90B requirements for entropy source

bull SP 800-90A deterministic algorithms bull SP 800-90C implement an RBG with -

90A and -90B components

Effect to FIPS 140

bull Current Requirement

ldquoCompromising the security of the key generation method (eg guessing the seed value to initialize the deterministic RNG) shall require as least as many operations as determining the value of the generated keyrdquo

Draft IG

bull First socialized last yearbull Entropy estimation mandatory forhellip

software modules which include entropy gathering mechanisms that are within the logical boundary of the module

Entropy Gathered within SW Module Logical Boundary

bull CMTL needs to submit entropy rationale

bull If DRBG is reseeded frequently the vendor shall make a reasonable heuristic claim of independence of the added entropy values

Entropy Gathered Outside the SW Module Logical

Boundarybull Entropy estimate should be in SP

1Entropy originates from another validated module

2Entropy originates from the operational environment

ChaosControl

bull Cryptographically secure DRBG

bull Available for mobile and desktop server environments

bull Compliant to 800-90 and draft FIPS 140 IG

Logical View of Entropy Sources for iOS Platform

Words from Whit

bull The right way to use tests in random number generation is to look for failure of the particular mechanism

bull Test each source independently (for stuck faults and other things that can be detected by correlation) and shut down if fewer than some threshold pass the test

Checks Performed

bull Entropy estimates for each source is recorded with that source

bull Exception reinitialize if not enough entropy

bull CRNGT (CREGT)

Initial Seeding

bull Ensures sufficient entropy before allowing clients to request random bytes

bull Checks for suitable amount of entropy before initialization

bull Seed file is persisted to disk

More about Tests

bull Heuristic bull log2 (max p(xi)) min-entropy from

800-90bbull Statistical Tests from 800-90bbull Full test suite documented by NIST

SP800-22rev1a

Results from 800-22rev1a

Statistical Analysis Results

Compression Bins CollisionOutput Space Size = 256Minimum Possible Score 0000000Maximum Possible Score 7183666Filename outbinTest name compressionOutput Space Size 256Number of samples 58321Number of events 57321Mean score 7139077Adjusted mean score 7126542Standard deviation 1818899Entropy type min-entropyEntropy estimate 4936194Entropyoutputdimension estimate 0617024

Output Space Size = 256Warning Shannon entropy estimate = 797Filename outbinTest name binsOutput Space Size 256Number of samples 58321Number of events 58321Mean score 0006927Adjusted mean score 0015471Standard deviation 0000000Entropy type min-entropyEntropy estimate 6014244Entropyoutputdimension estimate 0751781

Output Space Size = 256Minimum Possible Score 2000000Maximum Possible Score 20726106Filename outbinTest name collisionOutput Space Size 256Number of samples 58313Number of events 2803Mean score 20803782Adjusted mean score 20493429Standard deviation 9956489Entropy type min-entropyEntropy estimate 6103266Entropyoutputdimension estimate 0762908

Hey Guess Whathellip

bull ChaosControl is included with CryptoComply

bull ChaosControl is (nearly) patented

bull SafeLogic is offering it standalone at NO COST license until the end of Q1CY2015

Letrsquos Connect

bull SafeLogic

bull SafeLogic_Ray

bull wwwSafeLogiccom

  • Solving the Challenge of New Entropy Standards
  • Flow
  • Entropy
  • Practical Entropy
  • Entropy in the Real World
  • Entropy in Crypto
  • Issues
  • Entropy Quantified
  • NIST 800 Series
  • Effect to FIPS 140
  • Draft IG
  • Entropy Gathered within SW Module Logical Boundary
  • Entropy Gathered Outside the SW Module Logical Boundary
  • ChaosControl
  • Logical View of Entropy Sources for iOS Platform
  • Words from Whit
  • Checks Performed
  • Initial Seeding
  • More about Tests
  • Results from 800-22rev1a
  • Statistical Analysis Results
  • Hey Guess Whathellip
  • Letrsquos Connect
Page 4: Solving 800-90 Entropy Requirements in Software

Practical Entropy

S a f L og i c

Ru l s

Entropy in the Real World

Entropy in Crypto

bull Provide random bitsbull Challenges in authentication

protocolsbull Seeds for algorithmsbull Use to seed DRBG

bull Value is unpredictable output

Issues

bull Truly random data difficult impossible to generate on a computer

bull How to measure it

Entropy Quantified

bull log2 (max p(xi)) bull minus1113090 P(X = x)log P(X = x)

NIST 800 Series

bull SP 800-90B requirements for entropy source

bull SP 800-90A deterministic algorithms bull SP 800-90C implement an RBG with -

90A and -90B components

Effect to FIPS 140

bull Current Requirement

ldquoCompromising the security of the key generation method (eg guessing the seed value to initialize the deterministic RNG) shall require as least as many operations as determining the value of the generated keyrdquo

Draft IG

bull First socialized last yearbull Entropy estimation mandatory forhellip

software modules which include entropy gathering mechanisms that are within the logical boundary of the module

Entropy Gathered within SW Module Logical Boundary

bull CMTL needs to submit entropy rationale

bull If DRBG is reseeded frequently the vendor shall make a reasonable heuristic claim of independence of the added entropy values

Entropy Gathered Outside the SW Module Logical

Boundarybull Entropy estimate should be in SP

1Entropy originates from another validated module

2Entropy originates from the operational environment

ChaosControl

bull Cryptographically secure DRBG

bull Available for mobile and desktop server environments

bull Compliant to 800-90 and draft FIPS 140 IG

Logical View of Entropy Sources for iOS Platform

Words from Whit

bull The right way to use tests in random number generation is to look for failure of the particular mechanism

bull Test each source independently (for stuck faults and other things that can be detected by correlation) and shut down if fewer than some threshold pass the test

Checks Performed

bull Entropy estimates for each source is recorded with that source

bull Exception reinitialize if not enough entropy

bull CRNGT (CREGT)

Initial Seeding

bull Ensures sufficient entropy before allowing clients to request random bytes

bull Checks for suitable amount of entropy before initialization

bull Seed file is persisted to disk

More about Tests

bull Heuristic bull log2 (max p(xi)) min-entropy from

800-90bbull Statistical Tests from 800-90bbull Full test suite documented by NIST

SP800-22rev1a

Results from 800-22rev1a

Statistical Analysis Results

Compression Bins CollisionOutput Space Size = 256Minimum Possible Score 0000000Maximum Possible Score 7183666Filename outbinTest name compressionOutput Space Size 256Number of samples 58321Number of events 57321Mean score 7139077Adjusted mean score 7126542Standard deviation 1818899Entropy type min-entropyEntropy estimate 4936194Entropyoutputdimension estimate 0617024

Output Space Size = 256Warning Shannon entropy estimate = 797Filename outbinTest name binsOutput Space Size 256Number of samples 58321Number of events 58321Mean score 0006927Adjusted mean score 0015471Standard deviation 0000000Entropy type min-entropyEntropy estimate 6014244Entropyoutputdimension estimate 0751781

Output Space Size = 256Minimum Possible Score 2000000Maximum Possible Score 20726106Filename outbinTest name collisionOutput Space Size 256Number of samples 58313Number of events 2803Mean score 20803782Adjusted mean score 20493429Standard deviation 9956489Entropy type min-entropyEntropy estimate 6103266Entropyoutputdimension estimate 0762908

Hey Guess Whathellip

bull ChaosControl is included with CryptoComply

bull ChaosControl is (nearly) patented

bull SafeLogic is offering it standalone at NO COST license until the end of Q1CY2015

Letrsquos Connect

bull SafeLogic

bull SafeLogic_Ray

bull wwwSafeLogiccom

  • Solving the Challenge of New Entropy Standards
  • Flow
  • Entropy
  • Practical Entropy
  • Entropy in the Real World
  • Entropy in Crypto
  • Issues
  • Entropy Quantified
  • NIST 800 Series
  • Effect to FIPS 140
  • Draft IG
  • Entropy Gathered within SW Module Logical Boundary
  • Entropy Gathered Outside the SW Module Logical Boundary
  • ChaosControl
  • Logical View of Entropy Sources for iOS Platform
  • Words from Whit
  • Checks Performed
  • Initial Seeding
  • More about Tests
  • Results from 800-22rev1a
  • Statistical Analysis Results
  • Hey Guess Whathellip
  • Letrsquos Connect
Page 5: Solving 800-90 Entropy Requirements in Software

Entropy in the Real World

Entropy in Crypto

bull Provide random bitsbull Challenges in authentication

protocolsbull Seeds for algorithmsbull Use to seed DRBG

bull Value is unpredictable output

Issues

bull Truly random data difficult impossible to generate on a computer

bull How to measure it

Entropy Quantified

bull log2 (max p(xi)) bull minus1113090 P(X = x)log P(X = x)

NIST 800 Series

bull SP 800-90B requirements for entropy source

bull SP 800-90A deterministic algorithms bull SP 800-90C implement an RBG with -

90A and -90B components

Effect to FIPS 140

bull Current Requirement

ldquoCompromising the security of the key generation method (eg guessing the seed value to initialize the deterministic RNG) shall require as least as many operations as determining the value of the generated keyrdquo

Draft IG

bull First socialized last yearbull Entropy estimation mandatory forhellip

software modules which include entropy gathering mechanisms that are within the logical boundary of the module

Entropy Gathered within SW Module Logical Boundary

bull CMTL needs to submit entropy rationale

bull If DRBG is reseeded frequently the vendor shall make a reasonable heuristic claim of independence of the added entropy values

Entropy Gathered Outside the SW Module Logical

Boundarybull Entropy estimate should be in SP

1Entropy originates from another validated module

2Entropy originates from the operational environment

ChaosControl

bull Cryptographically secure DRBG

bull Available for mobile and desktop server environments

bull Compliant to 800-90 and draft FIPS 140 IG

Logical View of Entropy Sources for iOS Platform

Words from Whit

bull The right way to use tests in random number generation is to look for failure of the particular mechanism

bull Test each source independently (for stuck faults and other things that can be detected by correlation) and shut down if fewer than some threshold pass the test

Checks Performed

bull Entropy estimates for each source is recorded with that source

bull Exception reinitialize if not enough entropy

bull CRNGT (CREGT)

Initial Seeding

bull Ensures sufficient entropy before allowing clients to request random bytes

bull Checks for suitable amount of entropy before initialization

bull Seed file is persisted to disk

More about Tests

bull Heuristic bull log2 (max p(xi)) min-entropy from

800-90bbull Statistical Tests from 800-90bbull Full test suite documented by NIST

SP800-22rev1a

Results from 800-22rev1a

Statistical Analysis Results

Compression Bins CollisionOutput Space Size = 256Minimum Possible Score 0000000Maximum Possible Score 7183666Filename outbinTest name compressionOutput Space Size 256Number of samples 58321Number of events 57321Mean score 7139077Adjusted mean score 7126542Standard deviation 1818899Entropy type min-entropyEntropy estimate 4936194Entropyoutputdimension estimate 0617024

Output Space Size = 256Warning Shannon entropy estimate = 797Filename outbinTest name binsOutput Space Size 256Number of samples 58321Number of events 58321Mean score 0006927Adjusted mean score 0015471Standard deviation 0000000Entropy type min-entropyEntropy estimate 6014244Entropyoutputdimension estimate 0751781

Output Space Size = 256Minimum Possible Score 2000000Maximum Possible Score 20726106Filename outbinTest name collisionOutput Space Size 256Number of samples 58313Number of events 2803Mean score 20803782Adjusted mean score 20493429Standard deviation 9956489Entropy type min-entropyEntropy estimate 6103266Entropyoutputdimension estimate 0762908

Hey Guess Whathellip

bull ChaosControl is included with CryptoComply

bull ChaosControl is (nearly) patented

bull SafeLogic is offering it standalone at NO COST license until the end of Q1CY2015

Letrsquos Connect

bull SafeLogic

bull SafeLogic_Ray

bull wwwSafeLogiccom

  • Solving the Challenge of New Entropy Standards
  • Flow
  • Entropy
  • Practical Entropy
  • Entropy in the Real World
  • Entropy in Crypto
  • Issues
  • Entropy Quantified
  • NIST 800 Series
  • Effect to FIPS 140
  • Draft IG
  • Entropy Gathered within SW Module Logical Boundary
  • Entropy Gathered Outside the SW Module Logical Boundary
  • ChaosControl
  • Logical View of Entropy Sources for iOS Platform
  • Words from Whit
  • Checks Performed
  • Initial Seeding
  • More about Tests
  • Results from 800-22rev1a
  • Statistical Analysis Results
  • Hey Guess Whathellip
  • Letrsquos Connect
Page 6: Solving 800-90 Entropy Requirements in Software

Entropy in Crypto

bull Provide random bitsbull Challenges in authentication

protocolsbull Seeds for algorithmsbull Use to seed DRBG

bull Value is unpredictable output

Issues

bull Truly random data difficult impossible to generate on a computer

bull How to measure it

Entropy Quantified

bull log2 (max p(xi)) bull minus1113090 P(X = x)log P(X = x)

NIST 800 Series

bull SP 800-90B requirements for entropy source

bull SP 800-90A deterministic algorithms bull SP 800-90C implement an RBG with -

90A and -90B components

Effect to FIPS 140

bull Current Requirement

ldquoCompromising the security of the key generation method (eg guessing the seed value to initialize the deterministic RNG) shall require as least as many operations as determining the value of the generated keyrdquo

Draft IG

bull First socialized last yearbull Entropy estimation mandatory forhellip

software modules which include entropy gathering mechanisms that are within the logical boundary of the module

Entropy Gathered within SW Module Logical Boundary

bull CMTL needs to submit entropy rationale

bull If DRBG is reseeded frequently the vendor shall make a reasonable heuristic claim of independence of the added entropy values

Entropy Gathered Outside the SW Module Logical

Boundarybull Entropy estimate should be in SP

1Entropy originates from another validated module

2Entropy originates from the operational environment

ChaosControl

bull Cryptographically secure DRBG

bull Available for mobile and desktop server environments

bull Compliant to 800-90 and draft FIPS 140 IG

Logical View of Entropy Sources for iOS Platform

Words from Whit

bull The right way to use tests in random number generation is to look for failure of the particular mechanism

bull Test each source independently (for stuck faults and other things that can be detected by correlation) and shut down if fewer than some threshold pass the test

Checks Performed

bull Entropy estimates for each source is recorded with that source

bull Exception reinitialize if not enough entropy

bull CRNGT (CREGT)

Initial Seeding

bull Ensures sufficient entropy before allowing clients to request random bytes

bull Checks for suitable amount of entropy before initialization

bull Seed file is persisted to disk

More about Tests

bull Heuristic bull log2 (max p(xi)) min-entropy from

800-90bbull Statistical Tests from 800-90bbull Full test suite documented by NIST

SP800-22rev1a

Results from 800-22rev1a

Statistical Analysis Results

Compression Bins CollisionOutput Space Size = 256Minimum Possible Score 0000000Maximum Possible Score 7183666Filename outbinTest name compressionOutput Space Size 256Number of samples 58321Number of events 57321Mean score 7139077Adjusted mean score 7126542Standard deviation 1818899Entropy type min-entropyEntropy estimate 4936194Entropyoutputdimension estimate 0617024

Output Space Size = 256Warning Shannon entropy estimate = 797Filename outbinTest name binsOutput Space Size 256Number of samples 58321Number of events 58321Mean score 0006927Adjusted mean score 0015471Standard deviation 0000000Entropy type min-entropyEntropy estimate 6014244Entropyoutputdimension estimate 0751781

Output Space Size = 256Minimum Possible Score 2000000Maximum Possible Score 20726106Filename outbinTest name collisionOutput Space Size 256Number of samples 58313Number of events 2803Mean score 20803782Adjusted mean score 20493429Standard deviation 9956489Entropy type min-entropyEntropy estimate 6103266Entropyoutputdimension estimate 0762908

Hey Guess Whathellip

bull ChaosControl is included with CryptoComply

bull ChaosControl is (nearly) patented

bull SafeLogic is offering it standalone at NO COST license until the end of Q1CY2015

Letrsquos Connect

bull SafeLogic

bull SafeLogic_Ray

bull wwwSafeLogiccom

  • Solving the Challenge of New Entropy Standards
  • Flow
  • Entropy
  • Practical Entropy
  • Entropy in the Real World
  • Entropy in Crypto
  • Issues
  • Entropy Quantified
  • NIST 800 Series
  • Effect to FIPS 140
  • Draft IG
  • Entropy Gathered within SW Module Logical Boundary
  • Entropy Gathered Outside the SW Module Logical Boundary
  • ChaosControl
  • Logical View of Entropy Sources for iOS Platform
  • Words from Whit
  • Checks Performed
  • Initial Seeding
  • More about Tests
  • Results from 800-22rev1a
  • Statistical Analysis Results
  • Hey Guess Whathellip
  • Letrsquos Connect
Page 7: Solving 800-90 Entropy Requirements in Software

Issues

bull Truly random data difficult impossible to generate on a computer

bull How to measure it

Entropy Quantified

bull log2 (max p(xi)) bull minus1113090 P(X = x)log P(X = x)

NIST 800 Series

bull SP 800-90B requirements for entropy source

bull SP 800-90A deterministic algorithms bull SP 800-90C implement an RBG with -

90A and -90B components

Effect to FIPS 140

bull Current Requirement

ldquoCompromising the security of the key generation method (eg guessing the seed value to initialize the deterministic RNG) shall require as least as many operations as determining the value of the generated keyrdquo

Draft IG

bull First socialized last yearbull Entropy estimation mandatory forhellip

software modules which include entropy gathering mechanisms that are within the logical boundary of the module

Entropy Gathered within SW Module Logical Boundary

bull CMTL needs to submit entropy rationale

bull If DRBG is reseeded frequently the vendor shall make a reasonable heuristic claim of independence of the added entropy values

Entropy Gathered Outside the SW Module Logical

Boundarybull Entropy estimate should be in SP

1Entropy originates from another validated module

2Entropy originates from the operational environment

ChaosControl

bull Cryptographically secure DRBG

bull Available for mobile and desktop server environments

bull Compliant to 800-90 and draft FIPS 140 IG

Logical View of Entropy Sources for iOS Platform

Words from Whit

bull The right way to use tests in random number generation is to look for failure of the particular mechanism

bull Test each source independently (for stuck faults and other things that can be detected by correlation) and shut down if fewer than some threshold pass the test

Checks Performed

bull Entropy estimates for each source is recorded with that source

bull Exception reinitialize if not enough entropy

bull CRNGT (CREGT)

Initial Seeding

bull Ensures sufficient entropy before allowing clients to request random bytes

bull Checks for suitable amount of entropy before initialization

bull Seed file is persisted to disk

More about Tests

bull Heuristic bull log2 (max p(xi)) min-entropy from

800-90bbull Statistical Tests from 800-90bbull Full test suite documented by NIST

SP800-22rev1a

Results from 800-22rev1a

Statistical Analysis Results

Compression Bins CollisionOutput Space Size = 256Minimum Possible Score 0000000Maximum Possible Score 7183666Filename outbinTest name compressionOutput Space Size 256Number of samples 58321Number of events 57321Mean score 7139077Adjusted mean score 7126542Standard deviation 1818899Entropy type min-entropyEntropy estimate 4936194Entropyoutputdimension estimate 0617024

Output Space Size = 256Warning Shannon entropy estimate = 797Filename outbinTest name binsOutput Space Size 256Number of samples 58321Number of events 58321Mean score 0006927Adjusted mean score 0015471Standard deviation 0000000Entropy type min-entropyEntropy estimate 6014244Entropyoutputdimension estimate 0751781

Output Space Size = 256Minimum Possible Score 2000000Maximum Possible Score 20726106Filename outbinTest name collisionOutput Space Size 256Number of samples 58313Number of events 2803Mean score 20803782Adjusted mean score 20493429Standard deviation 9956489Entropy type min-entropyEntropy estimate 6103266Entropyoutputdimension estimate 0762908

Hey Guess Whathellip

bull ChaosControl is included with CryptoComply

bull ChaosControl is (nearly) patented

bull SafeLogic is offering it standalone at NO COST license until the end of Q1CY2015

Letrsquos Connect

bull SafeLogic

bull SafeLogic_Ray

bull wwwSafeLogiccom

  • Solving the Challenge of New Entropy Standards
  • Flow
  • Entropy
  • Practical Entropy
  • Entropy in the Real World
  • Entropy in Crypto
  • Issues
  • Entropy Quantified
  • NIST 800 Series
  • Effect to FIPS 140
  • Draft IG
  • Entropy Gathered within SW Module Logical Boundary
  • Entropy Gathered Outside the SW Module Logical Boundary
  • ChaosControl
  • Logical View of Entropy Sources for iOS Platform
  • Words from Whit
  • Checks Performed
  • Initial Seeding
  • More about Tests
  • Results from 800-22rev1a
  • Statistical Analysis Results
  • Hey Guess Whathellip
  • Letrsquos Connect
Page 8: Solving 800-90 Entropy Requirements in Software

Entropy Quantified

bull log2 (max p(xi)) bull minus1113090 P(X = x)log P(X = x)

NIST 800 Series

bull SP 800-90B requirements for entropy source

bull SP 800-90A deterministic algorithms bull SP 800-90C implement an RBG with -

90A and -90B components

Effect to FIPS 140

bull Current Requirement

ldquoCompromising the security of the key generation method (eg guessing the seed value to initialize the deterministic RNG) shall require as least as many operations as determining the value of the generated keyrdquo

Draft IG

bull First socialized last yearbull Entropy estimation mandatory forhellip

software modules which include entropy gathering mechanisms that are within the logical boundary of the module

Entropy Gathered within SW Module Logical Boundary

bull CMTL needs to submit entropy rationale

bull If DRBG is reseeded frequently the vendor shall make a reasonable heuristic claim of independence of the added entropy values

Entropy Gathered Outside the SW Module Logical

Boundarybull Entropy estimate should be in SP

1Entropy originates from another validated module

2Entropy originates from the operational environment

ChaosControl

bull Cryptographically secure DRBG

bull Available for mobile and desktop server environments

bull Compliant to 800-90 and draft FIPS 140 IG

Logical View of Entropy Sources for iOS Platform

Words from Whit

bull The right way to use tests in random number generation is to look for failure of the particular mechanism

bull Test each source independently (for stuck faults and other things that can be detected by correlation) and shut down if fewer than some threshold pass the test

Checks Performed

bull Entropy estimates for each source is recorded with that source

bull Exception reinitialize if not enough entropy

bull CRNGT (CREGT)

Initial Seeding

bull Ensures sufficient entropy before allowing clients to request random bytes

bull Checks for suitable amount of entropy before initialization

bull Seed file is persisted to disk

More about Tests

bull Heuristic bull log2 (max p(xi)) min-entropy from

800-90bbull Statistical Tests from 800-90bbull Full test suite documented by NIST

SP800-22rev1a

Results from 800-22rev1a

Statistical Analysis Results

Compression Bins CollisionOutput Space Size = 256Minimum Possible Score 0000000Maximum Possible Score 7183666Filename outbinTest name compressionOutput Space Size 256Number of samples 58321Number of events 57321Mean score 7139077Adjusted mean score 7126542Standard deviation 1818899Entropy type min-entropyEntropy estimate 4936194Entropyoutputdimension estimate 0617024

Output Space Size = 256Warning Shannon entropy estimate = 797Filename outbinTest name binsOutput Space Size 256Number of samples 58321Number of events 58321Mean score 0006927Adjusted mean score 0015471Standard deviation 0000000Entropy type min-entropyEntropy estimate 6014244Entropyoutputdimension estimate 0751781

Output Space Size = 256Minimum Possible Score 2000000Maximum Possible Score 20726106Filename outbinTest name collisionOutput Space Size 256Number of samples 58313Number of events 2803Mean score 20803782Adjusted mean score 20493429Standard deviation 9956489Entropy type min-entropyEntropy estimate 6103266Entropyoutputdimension estimate 0762908

Hey Guess Whathellip

bull ChaosControl is included with CryptoComply

bull ChaosControl is (nearly) patented

bull SafeLogic is offering it standalone at NO COST license until the end of Q1CY2015

Letrsquos Connect

bull SafeLogic

bull SafeLogic_Ray

bull wwwSafeLogiccom

  • Solving the Challenge of New Entropy Standards
  • Flow
  • Entropy
  • Practical Entropy
  • Entropy in the Real World
  • Entropy in Crypto
  • Issues
  • Entropy Quantified
  • NIST 800 Series
  • Effect to FIPS 140
  • Draft IG
  • Entropy Gathered within SW Module Logical Boundary
  • Entropy Gathered Outside the SW Module Logical Boundary
  • ChaosControl
  • Logical View of Entropy Sources for iOS Platform
  • Words from Whit
  • Checks Performed
  • Initial Seeding
  • More about Tests
  • Results from 800-22rev1a
  • Statistical Analysis Results
  • Hey Guess Whathellip
  • Letrsquos Connect
Page 9: Solving 800-90 Entropy Requirements in Software

NIST 800 Series

bull SP 800-90B requirements for entropy source

bull SP 800-90A deterministic algorithms bull SP 800-90C implement an RBG with -

90A and -90B components

Effect to FIPS 140

bull Current Requirement

ldquoCompromising the security of the key generation method (eg guessing the seed value to initialize the deterministic RNG) shall require as least as many operations as determining the value of the generated keyrdquo

Draft IG

bull First socialized last yearbull Entropy estimation mandatory forhellip

software modules which include entropy gathering mechanisms that are within the logical boundary of the module

Entropy Gathered within SW Module Logical Boundary

bull CMTL needs to submit entropy rationale

bull If DRBG is reseeded frequently the vendor shall make a reasonable heuristic claim of independence of the added entropy values

Entropy Gathered Outside the SW Module Logical

Boundarybull Entropy estimate should be in SP

1Entropy originates from another validated module

2Entropy originates from the operational environment

ChaosControl

bull Cryptographically secure DRBG

bull Available for mobile and desktop server environments

bull Compliant to 800-90 and draft FIPS 140 IG

Logical View of Entropy Sources for iOS Platform

Words from Whit

bull The right way to use tests in random number generation is to look for failure of the particular mechanism

bull Test each source independently (for stuck faults and other things that can be detected by correlation) and shut down if fewer than some threshold pass the test

Checks Performed

bull Entropy estimates for each source is recorded with that source

bull Exception reinitialize if not enough entropy

bull CRNGT (CREGT)

Initial Seeding

bull Ensures sufficient entropy before allowing clients to request random bytes

bull Checks for suitable amount of entropy before initialization

bull Seed file is persisted to disk

More about Tests

bull Heuristic bull log2 (max p(xi)) min-entropy from

800-90bbull Statistical Tests from 800-90bbull Full test suite documented by NIST

SP800-22rev1a

Results from 800-22rev1a

Statistical Analysis Results

Compression Bins CollisionOutput Space Size = 256Minimum Possible Score 0000000Maximum Possible Score 7183666Filename outbinTest name compressionOutput Space Size 256Number of samples 58321Number of events 57321Mean score 7139077Adjusted mean score 7126542Standard deviation 1818899Entropy type min-entropyEntropy estimate 4936194Entropyoutputdimension estimate 0617024

Output Space Size = 256Warning Shannon entropy estimate = 797Filename outbinTest name binsOutput Space Size 256Number of samples 58321Number of events 58321Mean score 0006927Adjusted mean score 0015471Standard deviation 0000000Entropy type min-entropyEntropy estimate 6014244Entropyoutputdimension estimate 0751781

Output Space Size = 256Minimum Possible Score 2000000Maximum Possible Score 20726106Filename outbinTest name collisionOutput Space Size 256Number of samples 58313Number of events 2803Mean score 20803782Adjusted mean score 20493429Standard deviation 9956489Entropy type min-entropyEntropy estimate 6103266Entropyoutputdimension estimate 0762908

Hey Guess Whathellip

bull ChaosControl is included with CryptoComply

bull ChaosControl is (nearly) patented

bull SafeLogic is offering it standalone at NO COST license until the end of Q1CY2015

Letrsquos Connect

bull SafeLogic

bull SafeLogic_Ray

bull wwwSafeLogiccom

  • Solving the Challenge of New Entropy Standards
  • Flow
  • Entropy
  • Practical Entropy
  • Entropy in the Real World
  • Entropy in Crypto
  • Issues
  • Entropy Quantified
  • NIST 800 Series
  • Effect to FIPS 140
  • Draft IG
  • Entropy Gathered within SW Module Logical Boundary
  • Entropy Gathered Outside the SW Module Logical Boundary
  • ChaosControl
  • Logical View of Entropy Sources for iOS Platform
  • Words from Whit
  • Checks Performed
  • Initial Seeding
  • More about Tests
  • Results from 800-22rev1a
  • Statistical Analysis Results
  • Hey Guess Whathellip
  • Letrsquos Connect
Page 10: Solving 800-90 Entropy Requirements in Software

Effect to FIPS 140

bull Current Requirement

ldquoCompromising the security of the key generation method (eg guessing the seed value to initialize the deterministic RNG) shall require as least as many operations as determining the value of the generated keyrdquo

Draft IG

bull First socialized last yearbull Entropy estimation mandatory forhellip

software modules which include entropy gathering mechanisms that are within the logical boundary of the module

Entropy Gathered within SW Module Logical Boundary

bull CMTL needs to submit entropy rationale

bull If DRBG is reseeded frequently the vendor shall make a reasonable heuristic claim of independence of the added entropy values

Entropy Gathered Outside the SW Module Logical

Boundarybull Entropy estimate should be in SP

1Entropy originates from another validated module

2Entropy originates from the operational environment

ChaosControl

bull Cryptographically secure DRBG

bull Available for mobile and desktop server environments

bull Compliant to 800-90 and draft FIPS 140 IG

Logical View of Entropy Sources for iOS Platform

Words from Whit

bull The right way to use tests in random number generation is to look for failure of the particular mechanism

bull Test each source independently (for stuck faults and other things that can be detected by correlation) and shut down if fewer than some threshold pass the test

Checks Performed

bull Entropy estimates for each source is recorded with that source

bull Exception reinitialize if not enough entropy

bull CRNGT (CREGT)

Initial Seeding

bull Ensures sufficient entropy before allowing clients to request random bytes

bull Checks for suitable amount of entropy before initialization

bull Seed file is persisted to disk

More about Tests

bull Heuristic bull log2 (max p(xi)) min-entropy from

800-90bbull Statistical Tests from 800-90bbull Full test suite documented by NIST

SP800-22rev1a

Results from 800-22rev1a

Statistical Analysis Results

Compression Bins CollisionOutput Space Size = 256Minimum Possible Score 0000000Maximum Possible Score 7183666Filename outbinTest name compressionOutput Space Size 256Number of samples 58321Number of events 57321Mean score 7139077Adjusted mean score 7126542Standard deviation 1818899Entropy type min-entropyEntropy estimate 4936194Entropyoutputdimension estimate 0617024

Output Space Size = 256Warning Shannon entropy estimate = 797Filename outbinTest name binsOutput Space Size 256Number of samples 58321Number of events 58321Mean score 0006927Adjusted mean score 0015471Standard deviation 0000000Entropy type min-entropyEntropy estimate 6014244Entropyoutputdimension estimate 0751781

Output Space Size = 256Minimum Possible Score 2000000Maximum Possible Score 20726106Filename outbinTest name collisionOutput Space Size 256Number of samples 58313Number of events 2803Mean score 20803782Adjusted mean score 20493429Standard deviation 9956489Entropy type min-entropyEntropy estimate 6103266Entropyoutputdimension estimate 0762908

Hey Guess Whathellip

bull ChaosControl is included with CryptoComply

bull ChaosControl is (nearly) patented

bull SafeLogic is offering it standalone at NO COST license until the end of Q1CY2015

Letrsquos Connect

bull SafeLogic

bull SafeLogic_Ray

bull wwwSafeLogiccom

  • Solving the Challenge of New Entropy Standards
  • Flow
  • Entropy
  • Practical Entropy
  • Entropy in the Real World
  • Entropy in Crypto
  • Issues
  • Entropy Quantified
  • NIST 800 Series
  • Effect to FIPS 140
  • Draft IG
  • Entropy Gathered within SW Module Logical Boundary
  • Entropy Gathered Outside the SW Module Logical Boundary
  • ChaosControl
  • Logical View of Entropy Sources for iOS Platform
  • Words from Whit
  • Checks Performed
  • Initial Seeding
  • More about Tests
  • Results from 800-22rev1a
  • Statistical Analysis Results
  • Hey Guess Whathellip
  • Letrsquos Connect
Page 11: Solving 800-90 Entropy Requirements in Software

Draft IG

bull First socialized last yearbull Entropy estimation mandatory forhellip

software modules which include entropy gathering mechanisms that are within the logical boundary of the module

Entropy Gathered within SW Module Logical Boundary

bull CMTL needs to submit entropy rationale

bull If DRBG is reseeded frequently the vendor shall make a reasonable heuristic claim of independence of the added entropy values

Entropy Gathered Outside the SW Module Logical

Boundarybull Entropy estimate should be in SP

1Entropy originates from another validated module

2Entropy originates from the operational environment

ChaosControl

bull Cryptographically secure DRBG

bull Available for mobile and desktop server environments

bull Compliant to 800-90 and draft FIPS 140 IG

Logical View of Entropy Sources for iOS Platform

Words from Whit

bull The right way to use tests in random number generation is to look for failure of the particular mechanism

bull Test each source independently (for stuck faults and other things that can be detected by correlation) and shut down if fewer than some threshold pass the test

Checks Performed

bull Entropy estimates for each source is recorded with that source

bull Exception reinitialize if not enough entropy

bull CRNGT (CREGT)

Initial Seeding

bull Ensures sufficient entropy before allowing clients to request random bytes

bull Checks for suitable amount of entropy before initialization

bull Seed file is persisted to disk

More about Tests

bull Heuristic bull log2 (max p(xi)) min-entropy from

800-90bbull Statistical Tests from 800-90bbull Full test suite documented by NIST

SP800-22rev1a

Results from 800-22rev1a

Statistical Analysis Results

Compression Bins CollisionOutput Space Size = 256Minimum Possible Score 0000000Maximum Possible Score 7183666Filename outbinTest name compressionOutput Space Size 256Number of samples 58321Number of events 57321Mean score 7139077Adjusted mean score 7126542Standard deviation 1818899Entropy type min-entropyEntropy estimate 4936194Entropyoutputdimension estimate 0617024

Output Space Size = 256Warning Shannon entropy estimate = 797Filename outbinTest name binsOutput Space Size 256Number of samples 58321Number of events 58321Mean score 0006927Adjusted mean score 0015471Standard deviation 0000000Entropy type min-entropyEntropy estimate 6014244Entropyoutputdimension estimate 0751781

Output Space Size = 256Minimum Possible Score 2000000Maximum Possible Score 20726106Filename outbinTest name collisionOutput Space Size 256Number of samples 58313Number of events 2803Mean score 20803782Adjusted mean score 20493429Standard deviation 9956489Entropy type min-entropyEntropy estimate 6103266Entropyoutputdimension estimate 0762908

Hey Guess Whathellip

bull ChaosControl is included with CryptoComply

bull ChaosControl is (nearly) patented

bull SafeLogic is offering it standalone at NO COST license until the end of Q1CY2015

Letrsquos Connect

bull SafeLogic

bull SafeLogic_Ray

bull wwwSafeLogiccom

  • Solving the Challenge of New Entropy Standards
  • Flow
  • Entropy
  • Practical Entropy
  • Entropy in the Real World
  • Entropy in Crypto
  • Issues
  • Entropy Quantified
  • NIST 800 Series
  • Effect to FIPS 140
  • Draft IG
  • Entropy Gathered within SW Module Logical Boundary
  • Entropy Gathered Outside the SW Module Logical Boundary
  • ChaosControl
  • Logical View of Entropy Sources for iOS Platform
  • Words from Whit
  • Checks Performed
  • Initial Seeding
  • More about Tests
  • Results from 800-22rev1a
  • Statistical Analysis Results
  • Hey Guess Whathellip
  • Letrsquos Connect
Page 12: Solving 800-90 Entropy Requirements in Software

Entropy Gathered within SW Module Logical Boundary

bull CMTL needs to submit entropy rationale

bull If DRBG is reseeded frequently the vendor shall make a reasonable heuristic claim of independence of the added entropy values

Entropy Gathered Outside the SW Module Logical

Boundarybull Entropy estimate should be in SP

1Entropy originates from another validated module

2Entropy originates from the operational environment

ChaosControl

bull Cryptographically secure DRBG

bull Available for mobile and desktop server environments

bull Compliant to 800-90 and draft FIPS 140 IG

Logical View of Entropy Sources for iOS Platform

Words from Whit

bull The right way to use tests in random number generation is to look for failure of the particular mechanism

bull Test each source independently (for stuck faults and other things that can be detected by correlation) and shut down if fewer than some threshold pass the test

Checks Performed

bull Entropy estimates for each source is recorded with that source

bull Exception reinitialize if not enough entropy

bull CRNGT (CREGT)

Initial Seeding

bull Ensures sufficient entropy before allowing clients to request random bytes

bull Checks for suitable amount of entropy before initialization

bull Seed file is persisted to disk

More about Tests

bull Heuristic bull log2 (max p(xi)) min-entropy from

800-90bbull Statistical Tests from 800-90bbull Full test suite documented by NIST

SP800-22rev1a

Results from 800-22rev1a

Statistical Analysis Results

Compression Bins CollisionOutput Space Size = 256Minimum Possible Score 0000000Maximum Possible Score 7183666Filename outbinTest name compressionOutput Space Size 256Number of samples 58321Number of events 57321Mean score 7139077Adjusted mean score 7126542Standard deviation 1818899Entropy type min-entropyEntropy estimate 4936194Entropyoutputdimension estimate 0617024

Output Space Size = 256Warning Shannon entropy estimate = 797Filename outbinTest name binsOutput Space Size 256Number of samples 58321Number of events 58321Mean score 0006927Adjusted mean score 0015471Standard deviation 0000000Entropy type min-entropyEntropy estimate 6014244Entropyoutputdimension estimate 0751781

Output Space Size = 256Minimum Possible Score 2000000Maximum Possible Score 20726106Filename outbinTest name collisionOutput Space Size 256Number of samples 58313Number of events 2803Mean score 20803782Adjusted mean score 20493429Standard deviation 9956489Entropy type min-entropyEntropy estimate 6103266Entropyoutputdimension estimate 0762908

Hey Guess Whathellip

bull ChaosControl is included with CryptoComply

bull ChaosControl is (nearly) patented

bull SafeLogic is offering it standalone at NO COST license until the end of Q1CY2015

Letrsquos Connect

bull SafeLogic

bull SafeLogic_Ray

bull wwwSafeLogiccom

  • Solving the Challenge of New Entropy Standards
  • Flow
  • Entropy
  • Practical Entropy
  • Entropy in the Real World
  • Entropy in Crypto
  • Issues
  • Entropy Quantified
  • NIST 800 Series
  • Effect to FIPS 140
  • Draft IG
  • Entropy Gathered within SW Module Logical Boundary
  • Entropy Gathered Outside the SW Module Logical Boundary
  • ChaosControl
  • Logical View of Entropy Sources for iOS Platform
  • Words from Whit
  • Checks Performed
  • Initial Seeding
  • More about Tests
  • Results from 800-22rev1a
  • Statistical Analysis Results
  • Hey Guess Whathellip
  • Letrsquos Connect
Page 13: Solving 800-90 Entropy Requirements in Software

Entropy Gathered Outside the SW Module Logical

Boundarybull Entropy estimate should be in SP

1Entropy originates from another validated module

2Entropy originates from the operational environment

ChaosControl

bull Cryptographically secure DRBG

bull Available for mobile and desktop server environments

bull Compliant to 800-90 and draft FIPS 140 IG

Logical View of Entropy Sources for iOS Platform

Words from Whit

bull The right way to use tests in random number generation is to look for failure of the particular mechanism

bull Test each source independently (for stuck faults and other things that can be detected by correlation) and shut down if fewer than some threshold pass the test

Checks Performed

bull Entropy estimates for each source is recorded with that source

bull Exception reinitialize if not enough entropy

bull CRNGT (CREGT)

Initial Seeding

bull Ensures sufficient entropy before allowing clients to request random bytes

bull Checks for suitable amount of entropy before initialization

bull Seed file is persisted to disk

More about Tests

bull Heuristic bull log2 (max p(xi)) min-entropy from

800-90bbull Statistical Tests from 800-90bbull Full test suite documented by NIST

SP800-22rev1a

Results from 800-22rev1a

Statistical Analysis Results

Compression Bins CollisionOutput Space Size = 256Minimum Possible Score 0000000Maximum Possible Score 7183666Filename outbinTest name compressionOutput Space Size 256Number of samples 58321Number of events 57321Mean score 7139077Adjusted mean score 7126542Standard deviation 1818899Entropy type min-entropyEntropy estimate 4936194Entropyoutputdimension estimate 0617024

Output Space Size = 256Warning Shannon entropy estimate = 797Filename outbinTest name binsOutput Space Size 256Number of samples 58321Number of events 58321Mean score 0006927Adjusted mean score 0015471Standard deviation 0000000Entropy type min-entropyEntropy estimate 6014244Entropyoutputdimension estimate 0751781

Output Space Size = 256Minimum Possible Score 2000000Maximum Possible Score 20726106Filename outbinTest name collisionOutput Space Size 256Number of samples 58313Number of events 2803Mean score 20803782Adjusted mean score 20493429Standard deviation 9956489Entropy type min-entropyEntropy estimate 6103266Entropyoutputdimension estimate 0762908

Hey Guess Whathellip

bull ChaosControl is included with CryptoComply

bull ChaosControl is (nearly) patented

bull SafeLogic is offering it standalone at NO COST license until the end of Q1CY2015

Letrsquos Connect

bull SafeLogic

bull SafeLogic_Ray

bull wwwSafeLogiccom

  • Solving the Challenge of New Entropy Standards
  • Flow
  • Entropy
  • Practical Entropy
  • Entropy in the Real World
  • Entropy in Crypto
  • Issues
  • Entropy Quantified
  • NIST 800 Series
  • Effect to FIPS 140
  • Draft IG
  • Entropy Gathered within SW Module Logical Boundary
  • Entropy Gathered Outside the SW Module Logical Boundary
  • ChaosControl
  • Logical View of Entropy Sources for iOS Platform
  • Words from Whit
  • Checks Performed
  • Initial Seeding
  • More about Tests
  • Results from 800-22rev1a
  • Statistical Analysis Results
  • Hey Guess Whathellip
  • Letrsquos Connect
Page 14: Solving 800-90 Entropy Requirements in Software

ChaosControl

bull Cryptographically secure DRBG

bull Available for mobile and desktop server environments

bull Compliant to 800-90 and draft FIPS 140 IG

Logical View of Entropy Sources for iOS Platform

Words from Whit

bull The right way to use tests in random number generation is to look for failure of the particular mechanism

bull Test each source independently (for stuck faults and other things that can be detected by correlation) and shut down if fewer than some threshold pass the test

Checks Performed

bull Entropy estimates for each source is recorded with that source

bull Exception reinitialize if not enough entropy

bull CRNGT (CREGT)

Initial Seeding

bull Ensures sufficient entropy before allowing clients to request random bytes

bull Checks for suitable amount of entropy before initialization

bull Seed file is persisted to disk

More about Tests

bull Heuristic bull log2 (max p(xi)) min-entropy from

800-90bbull Statistical Tests from 800-90bbull Full test suite documented by NIST

SP800-22rev1a

Results from 800-22rev1a

Statistical Analysis Results

Compression Bins CollisionOutput Space Size = 256Minimum Possible Score 0000000Maximum Possible Score 7183666Filename outbinTest name compressionOutput Space Size 256Number of samples 58321Number of events 57321Mean score 7139077Adjusted mean score 7126542Standard deviation 1818899Entropy type min-entropyEntropy estimate 4936194Entropyoutputdimension estimate 0617024

Output Space Size = 256Warning Shannon entropy estimate = 797Filename outbinTest name binsOutput Space Size 256Number of samples 58321Number of events 58321Mean score 0006927Adjusted mean score 0015471Standard deviation 0000000Entropy type min-entropyEntropy estimate 6014244Entropyoutputdimension estimate 0751781

Output Space Size = 256Minimum Possible Score 2000000Maximum Possible Score 20726106Filename outbinTest name collisionOutput Space Size 256Number of samples 58313Number of events 2803Mean score 20803782Adjusted mean score 20493429Standard deviation 9956489Entropy type min-entropyEntropy estimate 6103266Entropyoutputdimension estimate 0762908

Hey Guess Whathellip

bull ChaosControl is included with CryptoComply

bull ChaosControl is (nearly) patented

bull SafeLogic is offering it standalone at NO COST license until the end of Q1CY2015

Letrsquos Connect

bull SafeLogic

bull SafeLogic_Ray

bull wwwSafeLogiccom

  • Solving the Challenge of New Entropy Standards
  • Flow
  • Entropy
  • Practical Entropy
  • Entropy in the Real World
  • Entropy in Crypto
  • Issues
  • Entropy Quantified
  • NIST 800 Series
  • Effect to FIPS 140
  • Draft IG
  • Entropy Gathered within SW Module Logical Boundary
  • Entropy Gathered Outside the SW Module Logical Boundary
  • ChaosControl
  • Logical View of Entropy Sources for iOS Platform
  • Words from Whit
  • Checks Performed
  • Initial Seeding
  • More about Tests
  • Results from 800-22rev1a
  • Statistical Analysis Results
  • Hey Guess Whathellip
  • Letrsquos Connect
Page 15: Solving 800-90 Entropy Requirements in Software

Logical View of Entropy Sources for iOS Platform

Words from Whit

bull The right way to use tests in random number generation is to look for failure of the particular mechanism

bull Test each source independently (for stuck faults and other things that can be detected by correlation) and shut down if fewer than some threshold pass the test

Checks Performed

bull Entropy estimates for each source is recorded with that source

bull Exception reinitialize if not enough entropy

bull CRNGT (CREGT)

Initial Seeding

bull Ensures sufficient entropy before allowing clients to request random bytes

bull Checks for suitable amount of entropy before initialization

bull Seed file is persisted to disk

More about Tests

bull Heuristic bull log2 (max p(xi)) min-entropy from

800-90bbull Statistical Tests from 800-90bbull Full test suite documented by NIST

SP800-22rev1a

Results from 800-22rev1a

Statistical Analysis Results

Compression Bins CollisionOutput Space Size = 256Minimum Possible Score 0000000Maximum Possible Score 7183666Filename outbinTest name compressionOutput Space Size 256Number of samples 58321Number of events 57321Mean score 7139077Adjusted mean score 7126542Standard deviation 1818899Entropy type min-entropyEntropy estimate 4936194Entropyoutputdimension estimate 0617024

Output Space Size = 256Warning Shannon entropy estimate = 797Filename outbinTest name binsOutput Space Size 256Number of samples 58321Number of events 58321Mean score 0006927Adjusted mean score 0015471Standard deviation 0000000Entropy type min-entropyEntropy estimate 6014244Entropyoutputdimension estimate 0751781

Output Space Size = 256Minimum Possible Score 2000000Maximum Possible Score 20726106Filename outbinTest name collisionOutput Space Size 256Number of samples 58313Number of events 2803Mean score 20803782Adjusted mean score 20493429Standard deviation 9956489Entropy type min-entropyEntropy estimate 6103266Entropyoutputdimension estimate 0762908

Hey Guess Whathellip

bull ChaosControl is included with CryptoComply

bull ChaosControl is (nearly) patented

bull SafeLogic is offering it standalone at NO COST license until the end of Q1CY2015

Letrsquos Connect

bull SafeLogic

bull SafeLogic_Ray

bull wwwSafeLogiccom

  • Solving the Challenge of New Entropy Standards
  • Flow
  • Entropy
  • Practical Entropy
  • Entropy in the Real World
  • Entropy in Crypto
  • Issues
  • Entropy Quantified
  • NIST 800 Series
  • Effect to FIPS 140
  • Draft IG
  • Entropy Gathered within SW Module Logical Boundary
  • Entropy Gathered Outside the SW Module Logical Boundary
  • ChaosControl
  • Logical View of Entropy Sources for iOS Platform
  • Words from Whit
  • Checks Performed
  • Initial Seeding
  • More about Tests
  • Results from 800-22rev1a
  • Statistical Analysis Results
  • Hey Guess Whathellip
  • Letrsquos Connect
Page 16: Solving 800-90 Entropy Requirements in Software

Words from Whit

bull The right way to use tests in random number generation is to look for failure of the particular mechanism

bull Test each source independently (for stuck faults and other things that can be detected by correlation) and shut down if fewer than some threshold pass the test

Checks Performed

bull Entropy estimates for each source is recorded with that source

bull Exception reinitialize if not enough entropy

bull CRNGT (CREGT)

Initial Seeding

bull Ensures sufficient entropy before allowing clients to request random bytes

bull Checks for suitable amount of entropy before initialization

bull Seed file is persisted to disk

More about Tests

bull Heuristic bull log2 (max p(xi)) min-entropy from

800-90bbull Statistical Tests from 800-90bbull Full test suite documented by NIST

SP800-22rev1a

Results from 800-22rev1a

Statistical Analysis Results

Compression Bins CollisionOutput Space Size = 256Minimum Possible Score 0000000Maximum Possible Score 7183666Filename outbinTest name compressionOutput Space Size 256Number of samples 58321Number of events 57321Mean score 7139077Adjusted mean score 7126542Standard deviation 1818899Entropy type min-entropyEntropy estimate 4936194Entropyoutputdimension estimate 0617024

Output Space Size = 256Warning Shannon entropy estimate = 797Filename outbinTest name binsOutput Space Size 256Number of samples 58321Number of events 58321Mean score 0006927Adjusted mean score 0015471Standard deviation 0000000Entropy type min-entropyEntropy estimate 6014244Entropyoutputdimension estimate 0751781

Output Space Size = 256Minimum Possible Score 2000000Maximum Possible Score 20726106Filename outbinTest name collisionOutput Space Size 256Number of samples 58313Number of events 2803Mean score 20803782Adjusted mean score 20493429Standard deviation 9956489Entropy type min-entropyEntropy estimate 6103266Entropyoutputdimension estimate 0762908

Hey Guess Whathellip

bull ChaosControl is included with CryptoComply

bull ChaosControl is (nearly) patented

bull SafeLogic is offering it standalone at NO COST license until the end of Q1CY2015

Letrsquos Connect

bull SafeLogic

bull SafeLogic_Ray

bull wwwSafeLogiccom

  • Solving the Challenge of New Entropy Standards
  • Flow
  • Entropy
  • Practical Entropy
  • Entropy in the Real World
  • Entropy in Crypto
  • Issues
  • Entropy Quantified
  • NIST 800 Series
  • Effect to FIPS 140
  • Draft IG
  • Entropy Gathered within SW Module Logical Boundary
  • Entropy Gathered Outside the SW Module Logical Boundary
  • ChaosControl
  • Logical View of Entropy Sources for iOS Platform
  • Words from Whit
  • Checks Performed
  • Initial Seeding
  • More about Tests
  • Results from 800-22rev1a
  • Statistical Analysis Results
  • Hey Guess Whathellip
  • Letrsquos Connect
Page 17: Solving 800-90 Entropy Requirements in Software

Checks Performed

bull Entropy estimates for each source is recorded with that source

bull Exception reinitialize if not enough entropy

bull CRNGT (CREGT)

Initial Seeding

bull Ensures sufficient entropy before allowing clients to request random bytes

bull Checks for suitable amount of entropy before initialization

bull Seed file is persisted to disk

More about Tests

bull Heuristic bull log2 (max p(xi)) min-entropy from

800-90bbull Statistical Tests from 800-90bbull Full test suite documented by NIST

SP800-22rev1a

Results from 800-22rev1a

Statistical Analysis Results

Compression Bins CollisionOutput Space Size = 256Minimum Possible Score 0000000Maximum Possible Score 7183666Filename outbinTest name compressionOutput Space Size 256Number of samples 58321Number of events 57321Mean score 7139077Adjusted mean score 7126542Standard deviation 1818899Entropy type min-entropyEntropy estimate 4936194Entropyoutputdimension estimate 0617024

Output Space Size = 256Warning Shannon entropy estimate = 797Filename outbinTest name binsOutput Space Size 256Number of samples 58321Number of events 58321Mean score 0006927Adjusted mean score 0015471Standard deviation 0000000Entropy type min-entropyEntropy estimate 6014244Entropyoutputdimension estimate 0751781

Output Space Size = 256Minimum Possible Score 2000000Maximum Possible Score 20726106Filename outbinTest name collisionOutput Space Size 256Number of samples 58313Number of events 2803Mean score 20803782Adjusted mean score 20493429Standard deviation 9956489Entropy type min-entropyEntropy estimate 6103266Entropyoutputdimension estimate 0762908

Hey Guess Whathellip

bull ChaosControl is included with CryptoComply

bull ChaosControl is (nearly) patented

bull SafeLogic is offering it standalone at NO COST license until the end of Q1CY2015

Letrsquos Connect

bull SafeLogic

bull SafeLogic_Ray

bull wwwSafeLogiccom

  • Solving the Challenge of New Entropy Standards
  • Flow
  • Entropy
  • Practical Entropy
  • Entropy in the Real World
  • Entropy in Crypto
  • Issues
  • Entropy Quantified
  • NIST 800 Series
  • Effect to FIPS 140
  • Draft IG
  • Entropy Gathered within SW Module Logical Boundary
  • Entropy Gathered Outside the SW Module Logical Boundary
  • ChaosControl
  • Logical View of Entropy Sources for iOS Platform
  • Words from Whit
  • Checks Performed
  • Initial Seeding
  • More about Tests
  • Results from 800-22rev1a
  • Statistical Analysis Results
  • Hey Guess Whathellip
  • Letrsquos Connect
Page 18: Solving 800-90 Entropy Requirements in Software

Initial Seeding

bull Ensures sufficient entropy before allowing clients to request random bytes

bull Checks for suitable amount of entropy before initialization

bull Seed file is persisted to disk

More about Tests

bull Heuristic bull log2 (max p(xi)) min-entropy from

800-90bbull Statistical Tests from 800-90bbull Full test suite documented by NIST

SP800-22rev1a

Results from 800-22rev1a

Statistical Analysis Results

Compression Bins CollisionOutput Space Size = 256Minimum Possible Score 0000000Maximum Possible Score 7183666Filename outbinTest name compressionOutput Space Size 256Number of samples 58321Number of events 57321Mean score 7139077Adjusted mean score 7126542Standard deviation 1818899Entropy type min-entropyEntropy estimate 4936194Entropyoutputdimension estimate 0617024

Output Space Size = 256Warning Shannon entropy estimate = 797Filename outbinTest name binsOutput Space Size 256Number of samples 58321Number of events 58321Mean score 0006927Adjusted mean score 0015471Standard deviation 0000000Entropy type min-entropyEntropy estimate 6014244Entropyoutputdimension estimate 0751781

Output Space Size = 256Minimum Possible Score 2000000Maximum Possible Score 20726106Filename outbinTest name collisionOutput Space Size 256Number of samples 58313Number of events 2803Mean score 20803782Adjusted mean score 20493429Standard deviation 9956489Entropy type min-entropyEntropy estimate 6103266Entropyoutputdimension estimate 0762908

Hey Guess Whathellip

bull ChaosControl is included with CryptoComply

bull ChaosControl is (nearly) patented

bull SafeLogic is offering it standalone at NO COST license until the end of Q1CY2015

Letrsquos Connect

bull SafeLogic

bull SafeLogic_Ray

bull wwwSafeLogiccom

  • Solving the Challenge of New Entropy Standards
  • Flow
  • Entropy
  • Practical Entropy
  • Entropy in the Real World
  • Entropy in Crypto
  • Issues
  • Entropy Quantified
  • NIST 800 Series
  • Effect to FIPS 140
  • Draft IG
  • Entropy Gathered within SW Module Logical Boundary
  • Entropy Gathered Outside the SW Module Logical Boundary
  • ChaosControl
  • Logical View of Entropy Sources for iOS Platform
  • Words from Whit
  • Checks Performed
  • Initial Seeding
  • More about Tests
  • Results from 800-22rev1a
  • Statistical Analysis Results
  • Hey Guess Whathellip
  • Letrsquos Connect
Page 19: Solving 800-90 Entropy Requirements in Software

More about Tests

bull Heuristic bull log2 (max p(xi)) min-entropy from

800-90bbull Statistical Tests from 800-90bbull Full test suite documented by NIST

SP800-22rev1a

Results from 800-22rev1a

Statistical Analysis Results

Compression Bins CollisionOutput Space Size = 256Minimum Possible Score 0000000Maximum Possible Score 7183666Filename outbinTest name compressionOutput Space Size 256Number of samples 58321Number of events 57321Mean score 7139077Adjusted mean score 7126542Standard deviation 1818899Entropy type min-entropyEntropy estimate 4936194Entropyoutputdimension estimate 0617024

Output Space Size = 256Warning Shannon entropy estimate = 797Filename outbinTest name binsOutput Space Size 256Number of samples 58321Number of events 58321Mean score 0006927Adjusted mean score 0015471Standard deviation 0000000Entropy type min-entropyEntropy estimate 6014244Entropyoutputdimension estimate 0751781

Output Space Size = 256Minimum Possible Score 2000000Maximum Possible Score 20726106Filename outbinTest name collisionOutput Space Size 256Number of samples 58313Number of events 2803Mean score 20803782Adjusted mean score 20493429Standard deviation 9956489Entropy type min-entropyEntropy estimate 6103266Entropyoutputdimension estimate 0762908

Hey Guess Whathellip

bull ChaosControl is included with CryptoComply

bull ChaosControl is (nearly) patented

bull SafeLogic is offering it standalone at NO COST license until the end of Q1CY2015

Letrsquos Connect

bull SafeLogic

bull SafeLogic_Ray

bull wwwSafeLogiccom

  • Solving the Challenge of New Entropy Standards
  • Flow
  • Entropy
  • Practical Entropy
  • Entropy in the Real World
  • Entropy in Crypto
  • Issues
  • Entropy Quantified
  • NIST 800 Series
  • Effect to FIPS 140
  • Draft IG
  • Entropy Gathered within SW Module Logical Boundary
  • Entropy Gathered Outside the SW Module Logical Boundary
  • ChaosControl
  • Logical View of Entropy Sources for iOS Platform
  • Words from Whit
  • Checks Performed
  • Initial Seeding
  • More about Tests
  • Results from 800-22rev1a
  • Statistical Analysis Results
  • Hey Guess Whathellip
  • Letrsquos Connect
Page 20: Solving 800-90 Entropy Requirements in Software

Results from 800-22rev1a

Statistical Analysis Results

Compression Bins CollisionOutput Space Size = 256Minimum Possible Score 0000000Maximum Possible Score 7183666Filename outbinTest name compressionOutput Space Size 256Number of samples 58321Number of events 57321Mean score 7139077Adjusted mean score 7126542Standard deviation 1818899Entropy type min-entropyEntropy estimate 4936194Entropyoutputdimension estimate 0617024

Output Space Size = 256Warning Shannon entropy estimate = 797Filename outbinTest name binsOutput Space Size 256Number of samples 58321Number of events 58321Mean score 0006927Adjusted mean score 0015471Standard deviation 0000000Entropy type min-entropyEntropy estimate 6014244Entropyoutputdimension estimate 0751781

Output Space Size = 256Minimum Possible Score 2000000Maximum Possible Score 20726106Filename outbinTest name collisionOutput Space Size 256Number of samples 58313Number of events 2803Mean score 20803782Adjusted mean score 20493429Standard deviation 9956489Entropy type min-entropyEntropy estimate 6103266Entropyoutputdimension estimate 0762908

Hey Guess Whathellip

bull ChaosControl is included with CryptoComply

bull ChaosControl is (nearly) patented

bull SafeLogic is offering it standalone at NO COST license until the end of Q1CY2015

Letrsquos Connect

bull SafeLogic

bull SafeLogic_Ray

bull wwwSafeLogiccom

  • Solving the Challenge of New Entropy Standards
  • Flow
  • Entropy
  • Practical Entropy
  • Entropy in the Real World
  • Entropy in Crypto
  • Issues
  • Entropy Quantified
  • NIST 800 Series
  • Effect to FIPS 140
  • Draft IG
  • Entropy Gathered within SW Module Logical Boundary
  • Entropy Gathered Outside the SW Module Logical Boundary
  • ChaosControl
  • Logical View of Entropy Sources for iOS Platform
  • Words from Whit
  • Checks Performed
  • Initial Seeding
  • More about Tests
  • Results from 800-22rev1a
  • Statistical Analysis Results
  • Hey Guess Whathellip
  • Letrsquos Connect
Page 21: Solving 800-90 Entropy Requirements in Software

Statistical Analysis Results

Compression Bins CollisionOutput Space Size = 256Minimum Possible Score 0000000Maximum Possible Score 7183666Filename outbinTest name compressionOutput Space Size 256Number of samples 58321Number of events 57321Mean score 7139077Adjusted mean score 7126542Standard deviation 1818899Entropy type min-entropyEntropy estimate 4936194Entropyoutputdimension estimate 0617024

Output Space Size = 256Warning Shannon entropy estimate = 797Filename outbinTest name binsOutput Space Size 256Number of samples 58321Number of events 58321Mean score 0006927Adjusted mean score 0015471Standard deviation 0000000Entropy type min-entropyEntropy estimate 6014244Entropyoutputdimension estimate 0751781

Output Space Size = 256Minimum Possible Score 2000000Maximum Possible Score 20726106Filename outbinTest name collisionOutput Space Size 256Number of samples 58313Number of events 2803Mean score 20803782Adjusted mean score 20493429Standard deviation 9956489Entropy type min-entropyEntropy estimate 6103266Entropyoutputdimension estimate 0762908

Hey Guess Whathellip

bull ChaosControl is included with CryptoComply

bull ChaosControl is (nearly) patented

bull SafeLogic is offering it standalone at NO COST license until the end of Q1CY2015

Letrsquos Connect

bull SafeLogic

bull SafeLogic_Ray

bull wwwSafeLogiccom

  • Solving the Challenge of New Entropy Standards
  • Flow
  • Entropy
  • Practical Entropy
  • Entropy in the Real World
  • Entropy in Crypto
  • Issues
  • Entropy Quantified
  • NIST 800 Series
  • Effect to FIPS 140
  • Draft IG
  • Entropy Gathered within SW Module Logical Boundary
  • Entropy Gathered Outside the SW Module Logical Boundary
  • ChaosControl
  • Logical View of Entropy Sources for iOS Platform
  • Words from Whit
  • Checks Performed
  • Initial Seeding
  • More about Tests
  • Results from 800-22rev1a
  • Statistical Analysis Results
  • Hey Guess Whathellip
  • Letrsquos Connect
Page 22: Solving 800-90 Entropy Requirements in Software

Hey Guess Whathellip

bull ChaosControl is included with CryptoComply

bull ChaosControl is (nearly) patented

bull SafeLogic is offering it standalone at NO COST license until the end of Q1CY2015

Letrsquos Connect

bull SafeLogic

bull SafeLogic_Ray

bull wwwSafeLogiccom

  • Solving the Challenge of New Entropy Standards
  • Flow
  • Entropy
  • Practical Entropy
  • Entropy in the Real World
  • Entropy in Crypto
  • Issues
  • Entropy Quantified
  • NIST 800 Series
  • Effect to FIPS 140
  • Draft IG
  • Entropy Gathered within SW Module Logical Boundary
  • Entropy Gathered Outside the SW Module Logical Boundary
  • ChaosControl
  • Logical View of Entropy Sources for iOS Platform
  • Words from Whit
  • Checks Performed
  • Initial Seeding
  • More about Tests
  • Results from 800-22rev1a
  • Statistical Analysis Results
  • Hey Guess Whathellip
  • Letrsquos Connect
Page 23: Solving 800-90 Entropy Requirements in Software

Letrsquos Connect

bull SafeLogic

bull SafeLogic_Ray

bull wwwSafeLogiccom

  • Solving the Challenge of New Entropy Standards
  • Flow
  • Entropy
  • Practical Entropy
  • Entropy in the Real World
  • Entropy in Crypto
  • Issues
  • Entropy Quantified
  • NIST 800 Series
  • Effect to FIPS 140
  • Draft IG
  • Entropy Gathered within SW Module Logical Boundary
  • Entropy Gathered Outside the SW Module Logical Boundary
  • ChaosControl
  • Logical View of Entropy Sources for iOS Platform
  • Words from Whit
  • Checks Performed
  • Initial Seeding
  • More about Tests
  • Results from 800-22rev1a
  • Statistical Analysis Results
  • Hey Guess Whathellip
  • Letrsquos Connect

Information Theory and Statistics Lecture 1: Entropy …Entropy KL divergence Conditional entropy Mutual information Conditional MI Information Theory and Statistics Lecture 1: Entropy

Information Theory and Statistics Lecture 1: Entropy …Entropy KL divergence Conditional entropy Mutual information Conditional MI Information Theory and Statistics Lecture 1: Entropy

Entropy Basics

Entropy Basics

Comparison of Maximum Entropy and Higher-Order Entropy Estimators Amos ...fs2.american.edu/agolan/www/comparison.pdf · Comparison of Maximum Entropy and Higher-Order Entropy Estimators

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Conspiratorial Beliefs Observed through Entropy Principles (Entropy, 05.2015).pdf

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ENTROPY AND ART: THE VIEW BEYOND ARNHEIMmatilde/EntropyArtChapter.pdf · ENTROPY AND ART: THE VIEW BEYOND ARNHEIM 3 1. Thermodynamic Entropy The concept of entropy originates in Thermodynamics.

ENTROPY AND ART: THE VIEW BEYOND ARNHEIMmatilde/EntropyArtChapter.pdf · ENTROPY AND ART: THE VIEW BEYOND ARNHEIM 3 1. Thermodynamic Entropy The concept of entropy originates in Thermodynamics.

Pitzer Entropy

Pitzer Entropy

Nonequilibrium entropy and entropy distributions

Nonequilibrium entropy and entropy distributions

Information Entropy and Granulation Co–Entropy of ...

Information Entropy and Granulation Co–Entropy of ...

Entropy-Preserving and Entropy-Stable Relaxation IMEX and ...

Entropy-Preserving and Entropy-Stable Relaxation IMEX and ...

Entropy, Relative Entropy and Mutual Informationitct/slide/... · 2012-02-29 · Information Theory 8 Relative Entropy and Mutual Information The entropy of a random variable is a

Entropy, Relative Entropy and Mutual Informationitct/slide/... · 2012-02-29 · Information Theory 8 Relative Entropy and Mutual Information The entropy of a random variable is a

Information Entropy and Measures of Market Riskcentaur.reading.ac.uk/70371/1/entropy-19-00226.pdf · entropy Article Information Entropy and Measures of Market Risk Daniel Traian

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Sponaneity, Entropy, and Free Energy Entropy... · 2018. 4. 23. · Spontaneity, Entropy, and Free Energy. Entropy. Spontaneity Some processes occur spontaneously because the products

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Entropy andthesecondlaw

Entropy andthesecondlaw

VocabularyDivision Problem Solving $200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200 $600 $800 $400 $1000.

VocabularyDivision Problem Solving $200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200 $600 $800 $400 $1000.

Entropy of Keys and Password Generation Introduction to entropy Entropy and data compression Predictability of random number generation Entropy and system.

Entropy of Keys and Password Generation Introduction to entropy Entropy and data compression Predictability of random number generation Entropy and system.

SERRATION BEHAVIOR OF HIGH-ENTROPY ALLOYS (HEAs) Project ... · entropy alloys (LEAs), medium entropy alloys (MEAs), and high-entropy alloys (HEAs) through • To develop and test

SERRATION BEHAVIOR OF HIGH-ENTROPY ALLOYS (HEAs) Project ... · entropy alloys (LEAs), medium entropy alloys (MEAs), and high-entropy alloys (HEAs) through • To develop and test

Maximum entropy algorithm with inexact upper entropy bound

Maximum entropy algorithm with inexact upper entropy bound

Entropy Balance

Entropy Balance

Inaccessible Entropy I: Inaccessible Entropy Generators ...

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A NUMERICAL STUDY OF ENTROPY AND RESIDUAL ENTROPY ...

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