Abstract:
The security of the new information society that exchange data via modern intelligent
communication systems is nowadays very essential because of public connectivity
and the related threads (espionage or sabotage etc.). Many security product and
specially cryptographic systems (e.g., RSA, ElGamal, Diffie-Hellman, Elliptic
Curves cryptosystems, etc. ) was invented to encrypt and decrypt data, where the
security of such cryptosystems are based on the apparent intractability of solving
some number theoretic problems (e.g., The Discrete Logarithm Problem, Integer
Factorization Problem, Diffie-Hellman Problem, Quadratic Residuosity Problem,
Knapsack problem, etc.). Such problems are generally considered as being difficult
to solve if the associated parameters are carefully chosen. The Discrete Logarithm
Problem (DLP) on finite fields can be defined as followed: If we assume Zp
(denotes the set of integers {0, 1, 2, ....., p - 1}, where addition and multiplication
are performed modulo p) is a finite cyclic group of order p, where α a generator
of Zp and βεZp, then the Discrete Logarithm of
β to the base α, denoted loga β, is the unique
integer x, 0 <= x <= p-1, such that β = αx.
Many years this problem was studied but no known polynomial-time algorithm for
solving the Discrete Logarithm Problem (DLP) has been found. This study introduce
a new attack on the Discrete Logarithm Problem over finite fields- (