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

This work is protected by United States copyright laws and is

provided solely for the use of instructors in teaching their

courses and assessing student learning. Dissemination or sale of

any part of this work (including on the World Wide Web) will

destroy the integrity of the work and is not permitted. The work

and materials from it should never be made available to students

except by instructors using the accompanying text in their

classes. All recipients of this work are expected to abide by these

restrictions and to honor the intended pedagogical purposes and

the needs of other instructors who rely on these materials.

Stallings_8e_Accessible_fullppt_13.pdf

Stallings_8e_Accessible_fullppt_13.pdf

Related posts

HW