# lec9-4 - Diffie, Hellman, Elgamal Discrete Logarithm...

This preview shows pages 1–4. Sign up to view the full content.

Diffie, Hellman, Elgamal Discrete Logarithm Problem G : cyclic group of order p g : a generator of G Discrete logarithm problem Find log g ( h ) with non-negligible probability, for a uniform random h G Solver’s performance measured by success probability 2 Discrete Logarithm Problem Discrete logarithm assumption DL problem is hard: any solver which spends reasonable amount of time has only negligible success probability 3 Diffie-Hellman 1976: “New Directions in Cryptography” Many of modern ideas of PKC introduced Public-key encryption, one way function, digital signature, . .. Public-key based key exchange Securely share a symmetric key using only public channels 4

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
DH key exchange G : a cyclic group, with generator g Originally G = Z p * Alice: pick a and send g a to Bob Bob: pick b and send g b to Alice Both: compute g ab =( g a ) b =( g b ) a K = g ab : shared symmetric key 6 Security of DH First, some authentication necessary! Second, using g ab directly may not be good At least DL assumption necessary If a can be learned from g a , then g ab =( g b ) a In general, DL assumption not enough 7 Diffie-Hellman Problem Computational Diffie-Hellman problem: computing g xy , given g x and g y , for random x & y Computational Diffie-Hellman assumption: this is difficult on G 8
DL vs CDH CDH is easier: if DL can be solved then CDH can be too It is known that if G satisfies some mild conditions, CDH and DL are equivalent

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 10/21/2011 for the course CSCI 5471 taught by Professor Staff during the Spring '08 term at Minnesota.

### Page1 / 7

lec9-4 - Diffie, Hellman, Elgamal Discrete Logarithm...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online