Digital Signature

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Digital Signature

• Yuan Xue

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Hash function

• Hash function H
• h H(M)
• M is a message of variable length
• h is a fixed-length hash value
• H satisfies the following properties
• One-way property
• Weak collision resistance
• Strong collision resistance
• Widely used hash functions
• MD5
• SHA family (e.g. SHA-1, SHA-2)
• Usage
• Standalone
• With encryption algorithms
• Message Authentication
• Digital Signature

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Hash Function Usage

• Used Alone
• File integrity verification
• Public key fingerprint
• Passwd storage
• Combined with encryption functions
• Message Authentication
• HMAC
• Digital Signature

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Confidentiality and authentication
Authentication
Authentication, digital signature
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Authentication, digital signature, confidentiality
Authentication (no encryption needed!)
Authentication, confidentiality
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HMAC

• Hash function works with a symmetric key to
  provide message authentication
• Two methods

MAC
(1) MAC E K, H(M)
(2) MAC H MS ? Idea for HMAC
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HMAC Structure

• K K padded with 0
• on the left (b bits in total)
• ipad 00110110
• repeated b/8 times
• opad 01011100
• repeated b/8 times

36 in hex repeated
5C in hex repeated
HMAC(K,M) H(K?opad)H(K?ipad)M
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Digital Signature Overview

• Message Authentication Code
• Digital Signature
• Message authentication non-repudiation

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Digital Signature

• Two approaches

• Encryption of hash value via private key provides
  digital signature
• Any asymmetric encryption algorithm could be used
• E.g. RSA
• Many asymmetric encryption algorithms have export
  restriction
• DSA (digital signature algorithm)-based approach

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Digital Signature Algorithm

• Algorithm
• Based on discrete log operation
• Global variables
• p, q, g
• Private key x
• Public key y gx mod p
• User per-msg secret num k

• Digital Signature Algorithm
• An asymmetric key algorithm
• Can not be used for encryption
• Can ONLY be used for digital signature

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Key Exchange Algorithm

• Distribution of Secret Key using Public Key
  Algorithm
• Simple distribution
• With Authentication
• Diffie-Hellman

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Diffie-Hellman Key Exchange
a is a primitive root of prime number p then a
mod p, a2 mod p, , ap-1 mod p are distinct and
consist of the integers from 1 through p-1 For
any b and a primitive root a of p, unique
exponent I can be found such that b ai mod p
(0lti lt p-1)
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Public-Key Algorithm Summary
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MAC and DS Summary

• Message Authentication Code
• CBC-based
• Hash-based
• Encrypt the hash code
• Hash the message key
• HMAC
• Digital Signature
• Encrypt the hash code
• Digital signature standard

Symmetric Key Encryption
Asymmetric Key Encryption
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Comparison

• Computation efficiency
• Hash gt symmetric encryption gt asymmetric
  encryption
• Message Authentication Code
• CBC-based
• Hash-based
• Encrypt the hash code
• Hash the message key
• HMAC
• Digital Signature
• Encrypt the hash code
• Digital signature standard

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