DIGITAL SIGNATURES Fred Piper & Mert Özarar Codes & Ciphers Ltd 12 Duncan Road Richmond Surrey TW9...
-
date post
19-Dec-2015 -
Category
Documents
-
view
221 -
download
1
Transcript of DIGITAL SIGNATURES Fred Piper & Mert Özarar Codes & Ciphers Ltd 12 Duncan Road Richmond Surrey TW9...
DIGITAL SIGNATURES
Fred Piper & Mert Özarar
Codes & Ciphers Ltd12 Duncan RoadRichmondSurreyTW9 2JD
Information Security GroupRoyal Holloway, University of London
Egham, SurreyTW20 0EX
Digital Signatures 2
Outline
1. Brief Introduction to Cryptography
2. Public Key Systems
3. Basic Principles of Digital Signatures
4. Public Key Algorithms
5. Signing Processes
6. Arbitrated Signatures
7. Odds and Ends
NOTE: We will not cover all the sections
Digital Signatures 3
The Essence of Security
– Recognition of those you know
– Introduction to those you don’t
know
– Written signature
– Private conversation
Digital Signatures 4
The Challenge
• Transplant these basic social mechanisms to the telecommunications and/or business environment.
Digital Signatures 5
• Sender– Am I happy that the whole world sees this ?– Am I prepared to pay to stop them ?– Am I allowed to stop them ?
• Recipient– Do I have confidence in :
– the originator– the message contents and message stream– no future repudiation.
• Network Manager– Do I allow this user on to the network ?– How do I control their privileges ?
The Security Issues
Digital Signatures 6
Cryptography is used to provide:
1. Secrecy
2. Data Integrity
3. User Verification
4. Non-Repudiation
7Digital Signatures
Cipher System
cryptogramc
EncipheringAlgorithm
DecipheringAlgorithm
Key k(E) Key k(D)
messagem
messagem
Interceptor
Digital Signatures 8
The Attacker’s Perspective
DecipheringAlgorithm
Unknown Key
k(D)
Known c Wants m
Note: k(E) is not needed unlessit helps determine k(D)
Digital Signatures 9
Two Types of Cipher System
•Conventional or Symmetric–k(D) easily obtained from k(E)
•Public or Asymmetric–Computationally infeasible to
determine k(D) from k(E)
Digital Signatures 11
Public Key Systems
• Original Concept
• For a public key system an enciphering algorithm is
agreed and each would-be receiver publishes the key
which anyone may use to send a message to him.
• Thus for a public key system to be secure it must not be
possible to deduce the message from a knowledge of the
cryptogram and the enciphering key. Once such a system
is set up, a directory of all receivers plus their enciphering
keys is published. However, the only person to know any
given receiver’s deciphering key is the receiver himself.
Digital Signatures 12
Public Key Systems
• For a public key system, encipherment must be a ‘one-way function’ which has a ‘trapdoor’. The trapdoor must be a secret known only to the receiver.
• A ‘one-way function’ is one which is easy to perform but very difficult to reverse. A ‘trapdoor’ is a trick or another function which makes it easy to reverse the function
Digital Signatures 13
Some Mathematical One-Way Functions
1. Multiplication of two large primes.
2. Exponentiation modulo n ( n = pq ).
3. x ax in GF(2n) or GF(p).
4. k Ek(m) for fixed m where Ek is encryption in a symmetric key system which is secure against known plaintext attacks.
5. x a.x where x is an n-bit binary vector and a is a fixed n-tuple of integers. Thus a.x is an integer.
Digital Signatures 14
Public Key Cryptosystems
– Enable secure communications without exchanging secret keys
– Enable 3rd party authentication ( digital signature )
– Use number theoretic techniques– Introduce a whole new set of problems– Are extremely ingenious.
Digital Signatures 15
Digital Signatures
• According to ISO, the term Digital Signature is used: ‘to indicate a particular authentication technique used to establish the origin of a message in order to settle disputes of what message (if any) was sent’.
Digital Signatures 16
Digital Signatures
A signature on a message is some data that• validates a message and verifies its origin• a receiver can keep as evidence• a third party can use to resolve disputes.
It depends on• the message• a secret parameter only
available to the sender
It should be easy to compute
(by one person only) easy to verify difficult to forge
Digital Signatures 17
Digital Signature
• Cryptographic checksum
• Identifies sender
• Provides integrity check for data
• Can be checked by third party
Digital Signatures 18
Hand-Written Signatures
• Intrinsic to signer• Same on all documents• Physically attached to message• Beware plastic cards.
Digital Signatures• Use of secret parameter• Message dependent.
Digital Signatures 19
Principle of Digital Signatures
• There is a (secret) number which:
• Only one person can use
• Is used to identify that person
• ‘Anyone’ can verify that it has been used
NB: Anyone who knows the value of a number can use that number.
Digital Signatures 20
Attacks on Digital Signature Schemes
To impersonate A, I must either
• obtain A’s private key
• substitute my public key for A’s
NB: Similar attacks if A is receiving secret
data encrypted with A’s public key
Digital Signatures 21
Obtaining a Private Key
Mathematical attacks Physical attacks
NB: It may be sufficient to obtain a device which contains the key. Knowledge of actual value is not needed.
Digital Signatures 22
Certification Authority
AIM :To guarantee the authenticity of public keys.
METHOD :The Certification Authority guarantees the authenticity by signing a certificate containing user’s identity and public key with its secret key.
REQUIREMENT :All users must have an authentic copy of the Certification Authority’s public key.
Digital Signatures 23
Certification Process
Verifies credentials
CreatesCertificate
Receives(and checks)
Certificate
Presents Public Key and
credentials
Generates Key Set
Distribution
Centre
Owner
Digital Signatures 24
How Does it Work?
• The Certificate can accompany all Fred’s messages
• The recipient must directly or indirectly:• Trust the CA• Validate the certificate
The CA certifiesthat Fred Piper’s
public key is………..
Electronicallysigned by
the CA
Digital Signatures 25
User Authentication Certificates
• Ownership of certificate does not
establish identity
• Need protocols establishing use of
corresponding secret keys
Digital Signatures 26
WARNING
• Identity Theft
• You ‘are’ your private key
• You ‘are’ the private key corresponding to the public key in your certificiate
Digital Signatures 27
Certification Authorities
• Problems/Questions
• Who generates users’ keys?
• How is identity established?
• How can certificates be cancelled?
• Any others?
Digital Signatures 28
Fundamental Requirement
Internal infrastructure to support secure technological implementation
Digital Signatures 29
Is everything OK?
Announcement in Microsoft Security Bulletin MS01-017
“VeriSign Inc recently advised Microsoft that on January 29-30 2001 it issued two VeriSign Class 3 code-signing digital certificates to an individual who fraudulently claimed to be a Microsoft employee.”
Digital Signatures 30
How to Create a Digital Signature Using RSA
MESSAGE
HASHING FUNCTION
HASH OF MESSAGE
Sign using Private Key
SIGNATURE - SIGNED HASH OF MESSAGE
Digital Signatures 31
How to Verify a Digital Signature Using RSA
HASH OF MESSAGE
Verify theReceived Signature
Re-hash the Received Message
Verify using Public Key
Message
Hashing Function
HASH OF MESSAGE
MessageSignature
Signature
Message withAppended Signature
If hashes are equal, signature is authentic
Digital Signatures 32
Requirements for Hash Function h
(H1) condenses message M of arbitrary length into a fixed length ‘digest’ h(M)
(H2) is one-way
(H3) is collision free - it is computationally infeasible to construct messages M, M' with h(M) = h(M')
H3 implies a restriction on the size of h(M).
Digital Signatures 33
Diffie Hellman Key Establishment Protocol
General Idea: Use Public System
A and B exchange public keys: PA and PB
There is a publicly known function f which has 2 numbers as input and one number as output.
A computes f (SA, PB) where SA is A’s private key
B computes f (SB, PA) where SB is B’s private key
f is chosen so that f (SA, PB) = f (SB, PA)So A and B now share a (secret) number