This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: ICS 268: Cryptography and Communication Security 10/7/2004 Homework 2 Due Thursday , 10/14/2004 1 Prime Modular Arithmetics Let p be a prime. Recall groups Z p and Z * p from lecture and the handout on modular arithmetics. Recall the fact that Z * p is cyclic and has a generator (in fact it has many of them). Recall set QR p of squares modulo p . 1.1 Write out the elements of group Z 11 . How many elements are there? Pick an element g which is a generator of this group. For every element a Z 11 , write down DL ( g, 11) ( a ). 1.2 Let g be a generator of Z * p . Prove that if g x = g y mod p then x = y mod p 1. 1.3 Let g be a generator of Z * p . Prove that y QR p if and only if x = DL ( g,p ) ( y ) is even. (Note that since g is a generator then for every y Z * p there is x = DL ( g,p ) ( y ).) Which of the elements of Z 11 are squares? 1.4 Prove that y QR p if and only if y ( p 1) / 2 = 1 mod p ....
View
Full
Document
 Fall '04
 Jarecki

Click to edit the document details