Lecture4 – Introduction to Cryptography 2

Lecture4 – Introduction to Cryptography 2

Rice ELEC 528/ COMP 538

Farinaz Koushanfar

Spring 2009

Outline

• Public Key Encryption (PKE)– Motivation, characteristics of PKE, RSA (Rivest-

Shamir-Adelman) Encryption

• The Uses of Encryption– Cryptographic Hash Functions– Key Exchange– Digital Signatures– Certificates

Slides are courtesy of Leszek T. Lilien from WMichhttp://www.cs.wmich.edu/~llilien/

Motivation for PKE (1)

• So far - cryptosystems with secret keys

• Problems: – A lot of keys

• o(n2) keys for n users (n * (n-1) /2 keys)

— if each must be able to communicate with each

– Distributing so many keys securely

– Secure storage for the keys• User with n keys can’t just memorize them

• Can have a system with significantly fewer keys?

Yes!

Motivation for PKE (2)• 1976 — Diffie and Hellman — new kind of cryptosystem:

public key cryptosystem = asymmetric cryptosystem– Key pairs: < kPRIVATE, kPUBLIC>

– Each user owns one private key

– Each user shares the corresponding public key with n-1 remaining users => n users share each public key

– Only 2n keys for n users 2n = n * (1 + n * 1/n)» Since public key is shared by n people: 1 „owner” + (n-1) others = n

» 1/n since each part „owns” 1/n of the public key

• Even if each communicates with each

• Reduction from o(n2) to o(n) !

• n key pairs are:

<kPRIV-1, kPUB-1 >, <kPRIV-2, kPUB-2>, ..., <kPRIV-n, kPUB-n>

Characteristics of PKE (1)

PKE requirements1. It must be computationally easy to encipher or decipher a

message given the appropriate key

2. It must be computationally infeasible to derive kPRIV from kPUB

3. It must be computationally infeasible to determine kPRIV from a chosen plaintext attack

[cf. Barbara Endicott-Popovsky, U. Washington]

• Key pair characteristics

– One key is inverse of the other key of the pair

• i.e., it can undo encryption provided by the other:– D(kPRIV, E(kPUB, P)) = P

– D(kPUB, E(kPRIV, P)) = P

– One of the keys can be public since each key does only half of E ”+” D

• As shown above – need both E and D to get P back

Characteristics of PKE (2)

Characteristics of PKE (3)• Two E/D possibilities for key pair <kPRIV, kPUB >

– P = D(kPRIV, E(kPUB, P))

• User encrypts msg with kPUB (kPUB” ”locks”)

• Recipient decrypts msg with kPRIV (kPRIV ”unlocks”)

OR

– P = D(kPUB, E(kPRIV, P)) (e.g., in RSA)

• User encrypts msg with kPRIV (kPRIV ”locks”)

• Recipient decrypts msg with key kPUB (kPUB

”unlocks”)

• Do we still need symmetric encryption (SE) systems?

– Yes, PKEs are 10,000+ times (!) slower than SEs• PKEs use exponentiation – involves multiplication and division

• SEs use only bit operations (add, XOR< substitute, shift) – much faster

RSA Encryption (1)

• RSA = Rivest, Shamir, and Adelman (MIT), 1978

• Underlying hard problem:– Number theory – determining prime factors of a given (large)

number (ex. factoring of small #: 5 5, 6 2 *3)

– Arithmetic modulo n

• How secure is RSA?– So far remains secure (after all these years...)

– Will sb propose a quick algorithm to factor large numbers?

– Will quantum computing break it? TBD

RSA Encryption (2)

• In RSA:

P = E (D(P)) = D(E(P)) (order of D/E does not matter)

– More precisely: P = E(kE, D(kD, P)) = D(kD, E(kE, P))

• Encryption: C = Pe mod n KE = e

– Given C, it is very difficult to find P without knowing KD

• Decryption: P = Cd mod n KD = d

The Uses of Encryption

• PKE is much slower than SE (symmetric E)

– PKEs only for specialized, infrequent tasks

– SEs – a real workhorse

• Four applications of encryption (& outline) Cryptographic Hash Functions (subsec. 2H.1)

Key Exchange (subsec. 2H.2)

Digital Signatures (subsec. 2H.3)

Certificates (subsec. 2H.4)

Cryptographic Hash Functions (1)

• Integrity:– How can you be sure that a recived msg/doc was not modified

by an attacker or malfunction?

– Answer: use cryptography to ensure integrity

• Idea:– Wax seals on letters in Middle Ages

— easy to see if broken

– Cryptographic „seal” on doc/msg

— so that any change to it will be readily detected

Cryptographic Hash Fcns (2)

• A technique:

compute a hash fcn / checksum / msg digest

• More formally:– Problem: How to send n-bit msg so that R can easily

verify that it is intact

– Solution: Send a msg of n+k bits

• n bits — original msg

• k bits — checksum = msg digest

– Generated based on the n bits


Simple Parity for Error Detection (1)

• Simple (non-cryptographic) technique: parity – Add a single parity bit to detect if a message is correct– Example 1: odd parity

Force the block of data to have an odd # of 1’s• Data = 1011 — n = 4• Sent block = 10110 — n+k = 4+1

— looked at ‘1011’, added 0 to have odd # of 1’s

• Data = 0110• Sent block = 01101

— looked at ‘0110’, added 1 to have odd # of 1’s

– Example 2: ASCII parity bit• ASCII has 7 bits for data, 8th bit is single parity bit

– Either odd or even parity used

[cf. A. Striegel, U. Notre Dame]

• How parity enhances msg integrity?– Can detect error in 1 bit (or in odd # of bits)

– e,.g, if R gets 01001, R knows it’s wrong

(S sent 01101)

– Cannot detect error in 2 bits (or in even # of bits)

• Bec. parity stays OK -> undetectable integrity violation

– e.g, if R gets 01011, R knows it’s wrong

(S sent 01101)

– Cannot repair errors either

• E.g., R doesn’t know which bit in 01001 is wrong



Simple Parity for Error Detection (2)


Better Checksums against Errors & Attacks

• There are better checksums than simple odd/even parity

– Can detect multiple errors

– Can even repair multiple errors

• These checksums are to fix errors, not deal with attacks

• For attacks need

cryptographic checksums / strong hash functions


Strong Hash Function • Formal definition:

strong hash function (cryptographic checksum) is h: A -> B such that:

1) For any x A, h(x) is easy to compute2) For any y B, it is computationally infeasible to find

inverse of y, i.e., x A such that h(x) = y3) It is computationally infeasible to find a pair of colliding input

values, i.e. x, x’ A such that x ≠ x’ and h(x) = h(x’)Alternate (stronger) form for (3):Given any x A, it is computationally infeasible to findx’ A such that x ≠ x’ and h(x) = h(x’)

Due to (1) and (2), hash fcn is a one-way function

[cf. A. Striegel, U. Notre Dame, Barbara Endicott-Popovsky, U. Washington]


Collisions & Attacks on Msg Integrity (1)

• Note:– n bits of msg (x) mapped into k bits of its checksum (y)– k < n => collisions must exist– But it is computationally infeasible to find collisions for good

hash fcns

• Goal of a successful attack on msg integrity:– Change msg1 in such a way that checksum remains unchanged

(so R doesn’t detect the forgery)– I.e., find msg2 that collides with the original msg1 w.r.t.

checksum value• Finding msg2 is computationally infeasible (for good hash)

=> forging msg1 undetectably is computationally infeasible


• Pigeonhole principle– n containers for n+1 objects (n pigeonholes for n+1 pigeons)

=> at least 1 container will hold two objects

– Example: n = length(msg) = 5, k = length(hash)= 3 25=32 possible msgs vs. 23=8 possible hash values

=> at least 4 (= 32/8) different msgs hash into the same value (collisions!)

Real msgs and hash values are much longer than 5 or 3 bits!We know that collisions exist but:=> much tougher to find collisions=> much tougher to forge them



Collisions & Attacks on Msg Integrity (2)


File Checksum

• File checksum

– Calculated, a fcn defined on all bits of the file

– Result encrypted and stored with the file

– Each time file used by legitimate users, checksum recalculated, encrypted, stored with the file

• File sent to R

– When file received by R:

• R decrypts checksum c1 received in the file

• R independently calculates file checksum c2

• If c1 = c2 => file integrity is OK

• Otherwise – file integrity violated

• Keyed crypto checksum

– Key needed to compute checksum

– Keyed hash fcns DES, AES

• Use it in chaining mode:

link next msg block to value of the previous msg block» Example chaining: E(current block) XOR E(previous block)

=> connects block to all previous blocks

If file sent, file’s checksum could be the last block If chaining used, file checksum (=last block) depends on all previous

blocks => depends on all bits of the file


Keyed vs. Keyless Crypto Checksum (1)

• Keyed crypto checksum – CONT.

– Used for integrity + authentication

• Integrity: checksum makes msg modification difficult

• Authentication: only S and R know symmetric key

R: if msg integrity is OK, it must have been sent by S



• Keyless crypto checksum

– No key required to compute checksum

– Keyless hash functions

• MD5/MD4: any msg 128-bit digest (hash, checksum)

• SHA/SHS: any msg 160-bit digest

• Other: MD2, HAVAL, Snefru, ...

– Used for integrity (not authentication)

• Integrity: checksum makes msg modification difficult (with truly public key anybody can send msg, but nobody but S can easily modify this msg)

• No authentication: n (or all) people know public key –

R can’t prove which one of them sent a given msg[cf. A. Striegel, U. Notre Dame, Barbara Endicott-Popovsky, U. Washington]



• Motivation:

– X and Y don’t know each other

– X needs to send protected msg to Y• E.g., shopping on a web site

can do it if can securely exchange KE

• This is the problem of key exchange

– Important

– Hard

• Circular (chicken-’n-egg) problem?

„To establish secure session need secure channel”

• Circle can be broken – by public key cryptography– Can send public key even on insecure channel

Key Exchange (1)

• Given– S and R / kPRIV-S, kPUB-S -- kPRIV-R, kPUB-R

• Solution 1:– S determines secret key K– S encrypts K with kPRIV-S : C = E(kPRIV-S, K)

– S sends C to R

– R decrypts C to get K: D(kPUB-S, C) = K

– S & R communicate using secret (symmetric) key K

• BUT: Solution 1 is not good!!!– Question: Why?

Key Exchange (2)

Deriving Symmetric Key via PKE (2)

• Given– S and R / kPRIV-S, kPUB-S -- kPRIV-R, kPUB-R

• Solution 1:– S determines secret key K– S encrypts K with kPRIV-S: C = E(kPRIV-S, K)

– S sends C to R

– R decrypts C to get K: D(kPUB-S, C) = K


• BUT: Solution 1 is not good !!!– Answer:

Attacker who has kPUB-S can also perform decryption!

• The easier the more people know kPUB-S

• Trivial if kPUB-S is truly public

Key Exchange (3)


Key Exchange (4)


• Solution 2:– S determines secret key K– S encrypts K with kPUB-R: C = E(kPUB-R, K)– S sends C to R– R decrypts C to get K: D(kPRIV-R, C) = K– S & R communicate using secret (symmetric) key K

• Solution 2 is better– Only R can decode K (only R knows kPRIV-R)

• ...but Solution 2 still is not quite good– Question: Why?

• Hint: what about msg authentication?

Key Exchange (5)


• Solution 2:– S determines secret key K– S encrypts K with kPUB-R: C = E(kPUB-R , K)– S send C to R– R decrypts C to get K: D(kPRIV-R , C) = K


• Solution 2 is better– Only R can decode K (only R knows kPRIV-R)

• ...but Solution 2 still is not quite good– Answer:

No msg authentication(R has no assurance that msg was sent by S

– anybody could have encoded with kPUB-R)

Key Exchange (6)


• Solution 3:– S determines secret key K– S encrypts K with both kPRIV-S & kPUB-R :

C = E(kPUB-R , E(kPRIV-S, K))– S sends C to R– R decrypts C to get K:

D( kPUB-S , D(kPRIV-R, C) ) -- order important ! make sure you see this

(see Fig. 2-11 p.78)

• Solution 3 is good!– Only R can decode K (only R knows kPRIV-R)

– Authentication: R is assured that S sent C• Only S could have encoded K with kPRIV-S

Digital Signatures (1)

• Outline:– a. Problem Definition

– b. Properties of Electronic Signatures

– c. Using PKE for Digital Signatures

– d. Using Hash Fcns for Digital Signatures


Problem Definition (1)• Motivation:

– Need to sign and transmit electronic doc’s or msgs, incl. checks

• Analogous to signing & transmitting „paper” letters, doc’s, etc., incl. checks

• Roles of signatures (for both paper a& electronic)

– Proves unforgeability of doc/letter/check

– Authenticates person S who signed doc/letter/check

– Provides non-repudiation: S cannot say sb else signed it– Facilitates proving integrity (e.g., 2 signed legal copies for 2 parties)

– Note: signature might not identify the signing person

• if not legible

• Security requirements for digital signatures:

– Signature will not reveal signer’s private key

– Only owner of private key can produce a valid signature

– Verification of a correct signature succeeds

– Modification of a signed message can be detected

[cf. J. Leiwo]


Problem Definition (2)


Properties of Electronic Signatures (1)

• M – msg / Sg(S, M) – signature of S on M

Note: M = C or M = P

M = P – if authentication but no secrecy needed

• Required properties for electronic signatures:

– Unforgeable:

Only S can produce the pair [M, Sg(S, M)]

– Authenticable (can verify authenticity)/ non-repudiable:

R can verify that Sg(S,M) in [M, Sg(S, M)] comes from S

Only S could have produced M”+”Sg(S,M) Sg(S, M) is firmly attached to M

M

Sg(S, M)


Properties of Electronic Signatures (2)• Desirable properties for electr. signatures:

– Not alterable (assures „integrity”) :

Once sent, M”+”Sg(S,M) cannot be

undetectably altered by S, R, or interceptor

[I’d rather consider this a part of „unforgeability” above]

– Not reusable:

If M is received again, S detects that M is „old”– E.g., can’t deposit a copy of a check to „double-deposit”

• Digital signature is a protocol that mimics effect of signature on paper

M

Sg(S, M)


Using PKE for Digital Signatures (1)• Transmitting signed msgs with PKE

– Original message:

– Privacy transformation: C = E(P, KPUB-R)

• Only R can decrypt it (with KPRIV-R)

– Authenticity transformation = signing:

Sg = Sg(S, C) = D(C, KPRIV-S)

• Only S can produce Sg(S, C) (with KPRIV-S)

– Sent message:

Note: Remember that for some PKE algorithms (incl RSA):

D( E(M, _), _ ) = E( D(M, _), _ ) = M (commutativity of E-D)

C

Sg

P


Using PKE for Digital Signatures (3)• Properties:

[ C = E(P, KPUB-R) ]

[Sg = Sg(S, C) = D(C, KPRIV-S)]

• Unforgeability:

If C is forged,

it will not „correspond” to Sg ( i.e., E( Sg, KPUB-S) ≠ C )

• Authenticity:

If Sg is valid, S is authenticated (only S can produce valid S’s signature)

• Non-repudiation (undeniability):

If Sg is valid, only S could have produced it, and have sent C”+”Sg

C

Sg


Using PKE for Digital Signatures (2)• Transmitting signed msgs with PKE - cont.

– Received msg:[ C = E(P, KPUB-R) ]

[Sg = Sg(S, C) = D(C, KPRIV-S)]

– R verifies Sg with S’s public key KPUB-S:

If E( Sg, KPUB-S) = C, then signature is valid

– bec. E( Sg, KPUB-S) = E( D(C, KPRIV-S), KPUB-S) = C

– R decodes C with R’s private key KPRIV-R:

P = D(C, KPRIV-R)

C

Sg


Using Hash Fcns for Digital Signatures• Using hash fcn H in digital signatures

— signature over H(m), not over m length H(m) << length (m)

Before: Now:

[Fig — cf. J. Leiwo]

s = SgDA(x) = D(x, KPRIV-A)

EA(x) = E(x, KPUB-A)

Note:Any alteration of m is detected by B’s „Verify” step even if m is not encoded with KPUB-B —due to use of H(m)

m

Sg(S, H(m))

m

Sg(S, m)

m = P or m = C

Certificates (1)

• Outline– a. Introduction

– b. Trust Through a Common Respected Individual

– c. Certificates for Identity Authentication

– d. Trust Without a Single Hierarchy

Certificates (2)

Introduction (1)• Need for trust in human interactions

– Trust w.r.t.:• Individuals• Institutions (e.g., bank, hospital, car dealer)• Artifacts (e.g., car, Internet browser, software house)

• Trust in small village vs. big city– Small village: implicit trust

• Everybody knows everybody• Mr. X „feels” how much to trust Ms. Y

– Big city: need to consider trust explicitly• Ask around to find trusted entities

– Inquire friends, office mates, etc. about good car dealer, dentist, etc.

• Check „reputation databases”E.g., BBB=Better Business Bureau

Certificates (3)

Introduction (2)• Selected trust characteristics

– Trust comes in degrees of trust• Vs. binary trust (with a single trust threshold)

– Ubiquity of trust in social and artificial systems• Many users/computer systems err by trusting blindly (trust

without evidence or verification!)– E.g., OS trusts all application pgms – any allowed to run– E.g., sers trust unknown web sites with personal data

Certificates (4)

Introduction (3)• Basic means of building trust toward person / institution / artifact

X– Familiarity with X

• Person: face, voice, handwriting, etc.• Institution: company name, image, good will, etc• Artifact: manufacturer name, perceived quality, etc

– First-hand experience wih X’s activities/performance• Good or bad experience (trust or distrust grows)

– Reputation of X determined by evidence / credentialsReputation = second-hand knowledge of X’s actions/perf.

• Reputation databases (e.g., BBB, industry organizations, etc.) with „good” evidence or lack of „bad” evidence)

• Credentials: X’s driver license, library card, credit card

– Affiliation of X with person/institution/artifact Y• Trust/distrust toward Y rubs off on X

Certificates (5)

Introduction (4)• Basic means of verifying trust toward person / institution / artifact

X„Dovyeryay noh provyeryay” („Trust but verify”, a Russian proverb)

— Ronald Reagan (at the start of historic negotiations with Gornachev)

– Verify one’s experience• Check own notes about X’s activities/performance

– Verify reputation evidence / credentials• Call back to verify phone number• Check user feedback about quality of artifact (online)• Check reputation DB (e.g., consumer reports, BBB) for data

– Verify affiliation• Check with employer if X still employed• Check reputation of Y with which X is affiliated

Certificates (6)

Introduction (5)• Often trust is based on appearance of authenticity, without careful

verification– E.g., business order from Company A sent to company B– Order sent w/o careful verification of A by B– Why?

• Verification is expensive• Trust prevails in business• Risk of fraud or swindle is low• B might be „insured” against being cheated

– A trusted third-party intermediary assumes transaction risk» E.g., buyer’s bank guarantees a transaction payment

• Appearance of authenticity can be used by fraudster

Certificates (7)

Introduction (6)• Need similarly common and efficient/effective trust mechanisms

in the Cyber Space– Need somebody or something to:

assume risksOR

vouch for the other party

• A trusted third party is a basis for trust– When two interacting parties do not trust each other sufficiently

Trust Through Common Trusted Individual (1)

• Hierarchical structure of organizations

– CEO / Divisions/ Departments / Groups / Projects

– CEO doesn’t know engineers directly

– Still, CEO controls all via intermediate managers

=> hierarchy as basis for trust in an organization

• Example

– Ann meets Andy

– Andy claims he worksfor the same company

– Ann can verify via commontrusted individual / trusted third party (TTP) via Bill and Betty if Bill knows/trusts Betty via Bill and Camilla, otherwise

Camilla

BettyBill

Ann Andy


• Analogous approach for crypto key exchange

• Example– Ann and Andy want to comm-

unicate– Ann gives KPUB-Ann to Bill– Bill passes KPUB-Ann to Camilla

(or to Betty if he trusts her)

– Camilla passes KPUB-Ann to Betty– Betty passes KPUB-Ann to Andy

• Camilla is TTP (trusted third party)

Camilla

BettyBill

Ann Andy


• In reality need to pass more than just KPUB-Ann

– Every sender attaches an evidence of identity• Ann: Statement of Identity (SoI)• Bill, Camilla Betty: Transmittal of Identity (ToI)

– Andy receives KPUB-Ann with:• Ann’s proof of identity• Proof of identity for

all intermediaries• Proof that each inter-

mediary received KPUB-Ann

from trusted sender• E.g., Betty sends KPUB-Ann with the stmt:

„I am Betty and I received this key, SoI, and 2 ToIs from a person I know to be Camilla”

KPUB-Ann+SoI

KPUB-Ann+SoI+ToICamilla

BettyBill

Ann Andy

KPUB-Ann

+SoI +2 ToIs

KPUB-Ann

+SoI +3 ToIs


• In reality need to pass more than just KPUB-Ann – CONT.

– Andy can verify chain of evidence (SoI + ToI’s)

– This assures Andy that key was sent by Ann and not forged• Public key authentication

(delivered by trusted people)• Binding of key to Ann• Trustworthy Ann’s

identification as senderof this key

KPUB-Ann+SoI


BettyBill

Ann Andy

KPUB-Ann

+SoI +2 ToIs

KPUB-Ann

+SoI +3 ToIs


• Works pretty well within an org– There’s always sb common & trusted for any 2 employees (at

the top or below)

• Problems:1) If Bill, Camilla, or Betty

out of town, Ann &

Andy have to wait for

key exchange

2) Person at the top works

too hard to exchange all

keys quickly

KPUB-Ann+SoI


BettyBill

Ann Andy

KPUB-Ann

+SoI +2 ToIs

KPUB-Ann

+SoI +3 ToIs

Camilla

BettyBill

Ann Andy


• Protocol Solving Problem 1 (TTP absence): Idea: preauthenticated public key for (single) future use Ann asks Bill for complete chain from top down to her Bill provides chain: <Camilla, Bill, Ann> Ann requests for TOIs for her SOI ahead of time Ann receives from Bill 2 TOIs:

TOI#637: “I, Bill, gave this TOI to Ann to confirm her identityfor SOI#27” + Bill’s signature

TOI#5492: “I, Camilla, gave this TOIto Bill to confirm his identity forTOI#637” + Camilla’s signature

Ann can use SOI+TOIs any time

Think about full scenarioHint: Andy prepares his SOI+TOIs ahead of time


• Protocol Solving Problem 2 (TTP’s heavy workload): Idea: preauthenticated public key for unlimited future use Top TTP (e.g., a CEO) sends his TOIs to all Division Mgr

“I, Sushil, company CEO, attest to the identity of the Auto Division Mgr Diana, and I entrust Diana with attesting identities of her subordinates.”

Each Division Mgr sends TOIs to all Dept Mgrs E.g., “I, Diana, Auto Division Mgr, attest to the identity of the Engine

Dept Mgr Debbie, and I entrust Debbie with attesting identities of her subordinates.”

Note: Division Mgr is a TTP for all people working in her Division

…<intermediate levels>...


• Protocol Solving Problem 2 (TTP’s heavy workload):—CONT …<intermediate levels>... Each Group Leader sends TOIs to all Task Leaders

E.g., “I, Camille, Piston Group Leader, attest to the identity of the Piston Rings Task Leader Bill, and I entrust Bill with attesting identities of his subordinates.”

Note: Group Leader is a TTP for all people working in her Group

Each Task Leader sends TOIs to all his employees E.g., “I, Bill, Piston Rings Task Leader, attest to the identity of Piston

Rings Engineer Ann.” Note: Task Leader is a TTP for all people working on his Task

Chain: Sushil—Diana—…—Camilla—Bill—Ann

Good exercise: Think about protocol details –work out full scenario

Certificates to Authenticate Identity (1)

• Certificate for X

• TTP’s signature certifies trustworthiness of binding KPUB-X with X’s identity

– I.e., states that KPUB-X is really X’s public key

• How are certificates created?

Identifier of X

KPUB-X

TTP’s Signature


• Creating certificates for the company example– Sushil (CEO) (chain: Sushil—Diana—…—Camilla—Bill—Ann)

• Establishes <KPRIV-Sushil, KPUB-Sushil>

• Posts KPUB-Sushil for every Division Mgr to copy

• Receives request for certificate (encoded with KPUB-Sushil )

from Division Mgr X• Creates MX = <X, KPUB-X> (knows KPUB-X)

– E.g., MDiana = <‘Diana’, KPUB-Diana >

• Signs MX with SgSushil

SgSushil= D(MX, KPRIV-Sushil)

‘Diana’

KPUB-Diana

‘Diana’

KPUB-Diana

SgSushil


• Creating certificates ... example—CONT.

• Sushil encrypts MX and SgSushil with KPRIV-Sushil,producing certificate for Div.Mgr X:

CertX = E(<MX, SgSushil>, KPRIV-Sushil)– Note: Others can read certificate, but only its

issuer can update it!– E.g., produces certificate for Diana:

CertDiana = E(<MDiana, SgSushil>, KPRIV-Sushil)

• Sends certificate to Div. Mgr X

‘Diana’

KPUB-Diana

SgSushilCertDiana

(shading indicates encryption)

‘Diana’

KPUB-Diana

SgSushil

DIGRESSION—Note and understand these distinctions:

Using asymmetric cryptosystems:encrypt msg / sign msg / encrypt certificate

Encrypt msg – S encrypts (E) with R’s public key R decrypts msg with R’s private key

Sign msg – to sign a msg, S uses decryption algorithm D with S’s private key

R authenticates signature using encryption algorithm E with S’s public key

Encrypt certificate – after signing a (pre-)certificate, its issuer encrypts (E) the whole (pre-) certficate with his own private key Anybody who receives certificate can verify it by using decryption alg. D with

certificate issuers’ public keys But only certificate issuer can update a certificate she issued!


• Creating certificates ... example – CONT.– Diana (Div. Mgr) (chain: Sushil—Diana—…—Camilla—Bill—Ann)

• Establishes <KPRIV-Diana, KPUB-Diana>

• Posts KPUB-Diana for every subordinate to copy

• Sends request for certificate to her boss (Sushil) — as mentioned above (request encoded with KPUB-Sushil)

• Receives certificate from her boss CertDiana = E(<MDiana, SgSushil>, KPRIV-Sushil)

‘Diana’

KPUB-Diana

SgSushil


• Creating certificates ... example – CONT.• Diana receives request for certificate from Y, one of her

Dept Mgrs• Creates MY = <Y, KPUB-Y> (knows KPUB-Y)

– E.g., MDebbie = <‘Debbie’, KPUB-Debbie>• Signs MY with SgDiana

• Encrypts MY and signature with KPRIV-Diana,producing pre-certificate for Dept Mgr X:

preCertY = E(<MY, SgDiana>, KPRIV-Diana)

» E.g., produces pre-certificate for Debbie: preCertDebbie = E(<MDebbie, SgDiana>, KPRIV-

Diana)

‘Debbie’

SgDiana

KPUB-Debbie

preCertDebbie


• Creating certificates ... example – CONT.• Diana attaches to preCertY her own

certificate, producing certificate for Y: CertY = preCertY || CertDiana

– E.g., produces certificate for Debbie:

CertDebbie = preCertDebbie || CertDiana

• Sends Y’s certificate to Y

– ... <procedure repetead by all mgrsfrom the chain below Diana and above Bill>...

‘Debbie’

SgDiana

KPUB-Debbie

‘Diana’

SgSushil

KPUB-Diana

‘Debbie’

SgDiana

KPUB-Debbie

CertDebbie

—incl. Debbie’s preCert (top half encr. with KPRIV-Diana) and Diana’s Cert (bootom half encr. with KPRIV-Sushil)

preCertDebbie


• Creating certificates ... example – CONT.– Bill (Task Leader) (chain: Sushil—Diana—…—Camilla—Bill—Ann)

• Establishes <KPRIV-Bill, KPUB-Bill>

• Posts KPUB-Bill for every subordinate to copy

• Sends request for certificate to his boss (Camilla)(request encoded with KPUB-Camilla)

• Receives certificate from his boss (Camilla) CertBill = E(<MBill, SgCamilla>, KPRIV-Camilla)

‘Bill’

KPUB-Bill

SgCamilla


• Certificates for the company example – CONT.• Bill receives request for certificate from Z, one of his

Engineers• Creates MZ = <Z, KPUB-Z> (knows KPUB-Z)

– E.g., MAnn = <‘Ann’, KPUB-Ann>• Signs MZ with SgBill

• Encrypts MZ and signature with KPRIV-Bill,producing pre-certificate for Engineer Z:

preCertZ = E(<MZ, SgBill>, KPRIV-Bill)

» E.g., produces pre-certificate for Ann:preCertAnn = E(<MAnn, SgBill>, KPRIV-

Bill)

‘Ann’

KPUB-Ann

SgBill

preCertAnn


• Certificates for the company example – CONT.• Bill attaches his CertBill to preCertZ,

producing certificate for Z: CertZ = preCertZ || CertBill

– Can become loooong!

CertBill = preCertBill || CertCamilla =preCertBill || preCertCamilla || Cert... = preCertBill || preCertCamilla || ... || CertDebbie = preCertBill || preCertCamilla || ... || preCertDebbie || CertDiana

(cont.)

‘Ann’

KPUB-Ann

SgBill

preCertAnn


• Certificates for the company example – CONT.

– E.g., if the full certification chain is:Sushil—Diana—Debbie—Ahmet—

Camilla—Bill—Annthen the certificate for Ann is:

CertAnn = preCertAnn || preCertBill || preCertCamilla || preCertAhmet || preCertDebbie || CertDiana

» Notes:- Diana has Cert defined by CEO => no preCertDiana

- Cert’s become longer closer to the bottom of hierrarchy

• After creating CertZ, Bill sends it to Z– E.g., sends CertAnn to Ann

‘X’

KPUB-X

SgTTP_of_X

preCertX


• We don’t want such loooong certificates!

– Note:The taller hierarchy the longer certificates

– Solution: Flatten the certificate hierarchy• The ultimate: 1-level „hierarchy:

Everybody (in a given organization) gets certificates from a single trusted Certificate Authority (CA)

Note:If there is only single CA (not a chain of certifiers), there are no

pre-certificates, only (flat) certificates (signed by CA only)


• Requirements for a certification scheme:1) Any participant can read Cert to determine X and KPUB-X.

2) Any participant can verify that Cert originated from CA (Certificate Authority) and is not counterfeit.

3) Only CA can create and update Cert.4) Any participant can verify the currency of Cert.

To this end, each Cert must include a timestamp(not discussed by us).

• Q: Does our scheme satify these requirements?

[cf. Stallings - „Cryptography and Network Security”


• Requirements for a certification scheme:1) Any participant can read Cert to determine X and KPUB-X.

2) Any participant can verify that Cert originated from CA (Certificate Authority) and is not counterfeit.

3) Only CA can create and update Cert.4) Any participant can verify the currency of Cert.

• A to the Q: „Does our scheme satify these requirements?”1) Yes: Can decrypt with KPUB-CA.

2) Yes: If can be decrypted with KPUB-CA, must’ve been encrypted by CA.

3) Yes: Only CA can encrypt Cert with KPUB-CA.

4) No, but...: Our scheme included no timestamps – but can be extended.

[cf. Stallings - „Cryptography and Network Security”

Trust Without a Single Hierarchy (1)• Certificate structure relies on TTP at the top of certificate

hierarchy– TTP is not certified by anybody!– Must be very trustworthy

• If a „natural” hierarchy exists, certificate infrastructure can be based on it

– E.g., in a company

• Q: What if there is no „natural” hierarchy to use?– E.g., Web sites on the Internet

• A: Can designate a person/organization to vouch for authenticity of people or documents

– E.g., a notary public for legal documents– E.g., Registrar’s Office for grades

Trust Without a Single Hierarchy (2)• Q: How to find a trusted entity on the Internet?

– Not hierarchical organization• Despite hierarchy of naming

– No „top” entity

• A: Some entities that are widely trusted outside Cyberspace, create certification entities in the Cyberspace

– E.g., C&W HKT, SecureNet, Verisign, eTrust in US– Each one is at the „top”

• Each one has its users who trust it

• Different people, applications, etc., can and do use different TTPs (CAs) for certification

Trust Without a Single Hierarchy (3)• Considerations for key distribution protocols (such as the ones

involving TTP or CA):

– What are the operational restrictions?• E.g., need for 7/24 operation

– What are the trust requirements?

– How are failures dealt with?

– How efficient is the protocol?

– How easy to implement is the protocol?

– ...

[cf. J. Leiwo]

Remember and understand these distinctions:

Symmetric vs. asymmetric crypto systems Asymmetric used:

to provide secure channel for exchange of symmetric keys to encrypt vs. sign vs. whole certificate encryption

Asymmetric crypto system: Encrypt msg vs. sign msg vs. encrypt (pre-)certificate Encrypt msg – S encrypts (E) with R’s public key

R decrypts msg with R’s private key

Sign msg – to sign a msg, S uses decryption algorithm D with S’s private key R authenticates signature using encryption algorithm E with S’s

public key

Encrypt (pre-)certificate – after signing a (pre-)certificate, certificate issuer encrypts (E) the whole (pre-)certficate with his own private key Anybody who receives certificate can verify it by using decryption

alg. D with certificate issuers’ public keys But only certificate issuer can update certificates she issued!

Exercise scenarios to see you understand this well Symmetric/asymmetric crypto systems

Asymmetric used to exchange symmetric keys

Using asymmetric cryptosystems:

encrypt msg vs. sign msg vs. encrypt (pre-)certificate

Lecture4 – Introduction to Cryptography 2

Documents

Transcript of Lecture4 – Introduction to Cryptography 2