| Popis: |
The Discrete Log Problem (DLP), that is computing x, given y=@a^x and =G@?F"q^*, based Public Key Cryptosystem (PKC) have been studied since the late 1970's. Such development of PKC was possible because of the trapdoor function f:Z"@?->G= @?F"q^*, f(m)=@a^m is a group homomorphism. Due to this fact we have; Diffie Hellman (DH) type key exchange, ElGamal type message encryption, and Nyberg-Rueppel type digital signature protocols. The cryptosystems based on the trapdoor f(m)=@a^m are well understood and complete. However, there is another trapdoor function f:Z"@?->G, f(m)->Tr(@a^m), where G= @?F"q"^"k^*,k>=2, which needs more attention from researchers from a cryptographic protocols point of view. In the above mentioned case, although f is computable, it is not clear how to produce protocols such as Diffie Hellman type key exchange, ElGamal type message encryption, and Nyberg-Rueppel type digital signature algorithm, in general. It would be better, of course if we can find a more efficient algorithm than repeated squaring and trace to compute f(m)=Tr(@a^m) together with these protocols. In the literature we see some works for a more efficient algorithm to compute f(m)=Tr(@a^m) and not wondering about the protocols. We also see some works dealing with an efficient algorithm to compute Tr(@a^m) as well as discussing the cryptographic protocols. In this review paper, we are going to discuss the state of art on the subject. |
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