The Discrete Log Problem and Elliptic Curve Cryptography
نویسندگان
چکیده
In this paper, discrete log-based public-key cryptography is explored. Specifically, we first examine the Discrete Log Problem over a general cyclic group and algorithms that attempt to solve it. This leads us to an investigation of the security of cryptosystems based over certain specific cyclic groups: Fp, Fp , and the cyclic subgroup generated by a point on an elliptic curve; we ultimately see the highest security comes from using E(Fp) as our group. This necessitates an introduction of elliptic curves, which is provided. Finally, we conclude with cryptographic implementation considerations.
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