April 2016
Intermediate to advanced
461 pages
12h 1m
English
Content preview from Introduction to Cryptography with Open-Source Software
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124 Cryptography with Open-Source Software
[925932179882107407189545457216,
674060551589602342667719446404]
Now for the decryption:
sage: C[1]/C[0]^A
1000000000000000000000000000000
Security issues
The El Gamal cryptosystem is semantically secure if the decisional Diffie–
Hellman problem is assumed to hold in Z
p
. This assumption means that given
a primitive root a modulo p, there is no way to decide, given a
x
(mod p), a
y
(mod p) and a
z
(mod p), whether z = xy. In fact, in this mathematical
context of modular powers of primitive roots, the decisiona l Diffie–Hellman
problem re duces to the discrete logarithm problem. Diffie–Hellman problems
will be discussed in
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