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Good forums for advanced math?

C

Chu

Banned
Having difficuilty with some problems about Informatic-Theoritic security (in the sense of Shannon) and was wondering if anyone knows any good forums out there for advanced math?

-Chu
 
THis is supposed to be an easy problem, but for some reason it is giving me a ton of trouble
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Let p be a 128-bit prime and Z_p be the set of integers {0,...,p-1}. Consider the following encryption scheme. The secret pair of integers a,b EXISTSIN Z_p where a!=0. An encryption of a message M EXISTSIN Z_p is defined as:

E_(a,b)[M] = aM + b mod p

1. Show that when E is used to encrypt a message M EXISTSIN Z_p the system has perfect secrecy in the sense of shannon

2. Show that if the system is used to encrypt a plaintext (M_1,M_2), where M_1,M_2 EXISTIN Z_p, then the system does not have perfect security.
 
A few questions:

Are there specific things you have to show in order to prove the system has perfect secrety in the sense of shannon?

Say that I'm an enemy that wants to crack this encryption scheme. Initially, what do I know?
 
Sure, perfect secrecy in the sense of shannon simply means, that if K is your keyspace, C is your cypherspace, and P is your plaintext space, then :

Pr[P=M_0] = Pr[P=M_0 | C = C_0]

That notation can be translated into english as:

The probabilty that a random generated message is equal to M_0 must be equal to the probability that given any cyphertext C_0, M=M_0.

. . . and when typing that I think I just saw the solution so I might be kicking myself 😉
 
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