Unformatted text preview: roKnowledge Proofs of Knowledge ZeroKnowledge Proof of a Discrete Logarithm
Peggy wants to prove to Victor that she knows an x that satisfies Ax a B (mod p) where p is a prime, and x is a random number relatively prime to p  1. The numbers A, B, and p are public, and x is secret. Here’s how Peggy can prove she knows x without revealing it (see Section 5.1) [338,337]. (1) Peggy generates t random numbers, r1 , r2 , ..., rt, where all ri are less than p  1.1 (2) Peggy computes hi = Ari mod p, for all values of i, and sends them to Victor. (3) Peggy and Victor engage in a coinflipping protocol to generate t bits: b1, b2 , ..., bt. (4) For all t bits, Peggy does one of the following: a) If bi = 0, she sends Victor ri b) If bi = 1, she sends Victor si = (ri  rj) mod (p  1), where j is the lowest value for which bj = 1 (5) For all t bits, Victor confirms one of the following: a) If bi = 0, that Ari a hi (mod p) b) If bi = 1, that Asi a hihj1 (mod p) (6) Peggy sends Victor Z, where Z = (x  rj) mod (p  1) (7) Victor confirms that AZ a Bhj1 (mod p) Peggy’s probability of successfully cheating is 2t. ZeroKnowledge Proof of the Ability to Break RSA Alice knows Carol’s private key. Maybe she has broken RSA; maybe she has broken into Carol’s house and stolen the key. Alice wants to convince Bob that she knows Carol’s key. However, she doesn’t want to tell Bob the key or even decrypt one of Carol’s messages for Bob. Here’s a zeroknowledge protocol by which Alice convinces Bob that she knows Carol’s private key [888]. Previous Table of Contents Next Products  Contact Us  About Us  Privacy  Ad Info  Home Use of this site is subject to certain Terms & Conditions, Copyright © 19962000 EarthWeb Inc. All rights reserved. Reproduction whole or in part in any form or medium without express written permission of EarthWeb is prohibited. Read EarthWeb's privacy statement. To access the contents, click the chapter and section titles. Applied Cryptography, Second Edition: Protocols, Algorthms, and Source Code in C (cloth)
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This note was uploaded on 10/18/2010 for the course MATH CS 301 taught by Professor Aliulger during the Fall '10 term at Koç University.
 Fall '10
 ALIULGER
 Cryptography

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