Public Key Cryptosystem and Binary Edwards Curves on the Ring |
Moha ben taleb Elhamam, Abdelhakim Chillali, Lhoussain El Fadil FSDM Sidi Mohamed Ben Abdellah University Fez, Morocco., FP, LSI Sidi Mohamed Ben Abdellah University Taza, Morocco., FSDM Sidi Mohamed Ben Abdellah University Fez, Morocco. |
Abstract: Let be a finite ring of characteristic 2, where e2 = e and n is a positive integer. Let (a, d) 2 ( )2, such that a and d + a2 + a are invertible in , we study the binary Edwards curve over this ring, denoted by and we give a bijection between this curve and produces two binary Edwards curves defined on the finite field . Afterthat we study the addition law of binary Edwards curves over the ring . We end this work with cryptography applications, ElGamal twisted Edwards curve cryptosystem and Cramer-Shoup twisted Edwards curve cryptosystem. |
Keywords: Binary Edwards curves, Addition law, Finite Ring, Finite Field, Local Ring, Cryptography, encryption, decryption Public Key Cryptosystem and Binary Edwards Curves on the Ring |
DOI:https://doi.org/10.6025/jdim/2022/20/1/25-30 |
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References: [1] Harold M. Edwards. (2007). Normal form for elliptic curves. Bulletin of the American Mathematical Society, 44 (3) 393-423, April. |