So if there were a full house and every fan tossed a coin, guessing the
discrete logarithm would be as hard as correctly guessing every single coin toss."
[8] proposed a new authentication scheme based on the computational difficulty of
discrete logarithm problem (DLP), nevertheless, their scheme is demonstrated to be subject to the Denning-Sacco attack and stolen verifier attack [9].
The topics include generic Newton polygons for curves of given p-rank, the
discrete logarithm problem with auxiliary inputs, a garden of curves with many automorphisms, permutations of finite fields and uniform distribution modulo 1, and an analog of the Kronecker-Weger theorem in positive characteristic.
The security of ECC based protocols depend on the difficulty of solving Elliptic Curve
Discrete Logarithm Problem (ECDLP), Elliptic Curve Computational Diffie-Hellman Problem (ECCDHP) and Elliptic Curve Decisional Diffie-Hellman Problem (ECDDHP).
Knowing n, g, [g.sup.A] mod n, and [g.sup.C] mod n, anyone trying to decrypt messages needs to solve a difficult
discrete logarithm problem to determine A or C.