Stallings_8e_Accessible_fullppt_13.pdf

Cryptography and Network Security:

Principles and PracticeEighth Edition

Chapter 13

Digital Signatures

Figure 13.1 Simplified Depiction of

Essential Elements of Digital

Signature Process

Digital Signature Properties

• It must verify the author and the date and time of the

signature

• It must authenticate the contents at the time of the

signature

• It must be verifiable by third parties to resolve disputes

Attacks

• Key-only attack

– C only knows A’s public key

• Known message attack

– C is given access to a set of messages and their signatures

• Generic chosen message attack

– C chooses a list of messages before attempting to break A’s signature scheme, independent of A’s public key; C then obtains from A valid signatures for the chosen messages

• Directed chosen message attack

– Similar to the generic attack, except that the list of messages to be signed is chosen after C knows A’s public key but before any signatures are seen

• Adaptive chosen message attack

– C may request from A signatures of messages that depend on previously obtained message-signature pairs

Forgeries

• Total break

– C determines A’s private key

• Universal forgery

– C finds an efficient signing algorithm that provides an

equivalent way of constructing signatures on arbitrary

messages

• Selective forgery

– C forges a signature for a particular message chosen

by C

• Existential forgery

– C forges a signature for at least one message; C has

no control over the message

Digital Signature Requirements

• The signature must be a bit pattern that depends on the

message being signed

• The signature must use some information unique to the sender

to prevent both forgery and denial

• It must be relatively easy to produce the digital signature

• It must be relatively easy to recognize and verify the digital

signature

• It must be computationally infeasible to forge a digital signature,

either by constructing a new message for an existing digital

signature or by constructing a fraudulent digital signature for a

given message

• It must be practical to retain a copy of the digital signature in

storage

Direct Digital Signature

• Refers to a digital signature scheme that involves only the communicating

parties

– It is assumed that the destination knows the public key of the source

• Confidentiality can be provided by encrypting the entire message plus

signature with a shared secret key

– It is important to perform the signature function first and then an outer

confidentiality function

– In case of dispute some third party must view the message and its

signature

• The validity of the scheme depends on the security of the sender’s private key

– If a sender later wishes to deny sending a particular message, the sender

can claim that the private key was lost or stolen and that someone else

forged his or her signature

– One way to thwart or at least weaken this ploy is to require every signed

message to include a timestamp and to require prompt reporting of

compromised keys to a central authority

ElGamal Digital Signature

• Scheme involves the use of the private key for encryption

and the public key for decryption

• Global elements are a prime number q and a, which is a

primitive root of q

• Use private key for encryption (signing)

• Uses public key for decryption (verification)

• Each user generates their key

– Chooses a secret key (number): 1 < xA < q-1

– Compute their public key: yA = axA mod q

Schnorr Digital Signature

• Scheme is based on discrete logarithms

• Minimizes the message-dependent amount of computation

required to generate a signature

– Multiplying a 2n-bit integer with an n-bit integer

• Main work can be done during the idle time of the

processor

• Based on using a prime modulus p, with p – 1 having a

prime factor q of appropriate size

– Typically p is a 1024-bit number, and q is a 160-bit

number

N I S T Digital Signature Algorithm

• Published by N I S T as Federal Information Processing

Standard F I P S 186

• Makes use of the Secure Hash Algorithm (S H A)

• The latest version, F I P S 186-3, also incorporates digital

signature algorithms based on R S A and on elliptic curve

cryptography

Figure 13.2 Two Approaches to

Digital Signatures

Figure 13.3 The Digital Signature

Algorithm (D S A)

Figure 13.4 D S A Signing and Verifying

Elliptic Curve Digital Signature

Algorithm (E C D S A)

• Four elements are involved:

– All those participating in the digital signature scheme use

the same global domain parameters, which define an elliptic

curve and a point of origin on the curve

– A signer must first generate a public, private key pair

– A hash value is generated for the message to be signed;

using the private key, the domain parameters, and the hash

value, a signature is generated

– To verify the signature, the verifier uses as input the signer’s

public key, the domain parameters, and the integer s; the

output is a value v that is compared to r ; the signature is

verified if the v = r

Figure 13.5 E C D S A Signing and

Verifying

R S A-P S S

• R S A Probabilistic Signature Scheme

• Included in the 2009 version of F I P S 186

• Latest of the R S A schemes and the one that R S A Laboratories

recommends as the most secure of the R S A schemes

• For all schemes developed prior to P S S it has not been possible

to develop a mathematical proof that the signature scheme is as

secure as the underlying R S A encryption/decryption primitive

• The PSS approach was first proposed by Bellare and Rogaway

• This approach, unlike the other R S A-based schemes,

introduces a randomization process that enables the security of

the method to be shown to be closely related to the security of

the R S A algorithm itself

Mask Generation Function (M G F)

• Typically based on a secure cryptographic hash function

such as S H A-1

– Is intended to be a cryptographically secure way of

generating a message digest, or hash, of variable

length based on an underlying cryptographic hash

function that produces a fixed-length output

Figure 13.6 R S A-P S S Encoding

Figure 13.7 R S A-P S S E M Verification

Summary

• Present an overview of the digital signature process

• Understand the ElGamal digital signature scheme

• Understand the Schnorr digital signature scheme

• Understand the N I S T digital signature scheme

• Compare and contrast the N I S T digital signature scheme

with the ElGamal and Schnorr digital signature schemes

• Understand the elliptic curve digital signature scheme

• Understand the R S A-P S S digital signature scheme

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