MA-410 Homework 4
Due at the beginning of class,
Wednesday, April 23, 2008
Solutions may be submitted in person in class,
or you may email an ASCII text,
html, or postscipt/pdf-formatted document to me.
Note my office hours on my
schedule.
- Show that the El Gamal public key crpytosystem
is malleable even if Alice encrypts with a randomly chosen r every time.
For the example p = 13, g = 2, s = 6, show how
Charlie can encrypt M/2 with his own random r'
seeing Alice's ciphertext of M which is assumed to be an even residue.
- Let p be an odd prime such that 3 does not
divide p-1. Prove that for any residue a modulo
p there exists a residue b modulo p such
that b3 is congruent to a modulo p.
- ENT, §9.3, Problem 1(d), page 190. Please use Eisenstein's method.
- ENT, §12.1, Problem 4, page 251.