Generation and Implementation of Cryptographically Strong Elliptic Curves
[Referat wygłoszony na: konferencji NuTMiC - Number Theory Mathods and Cryptography, Wraszawa, Instytut Matematyki Uniwersytetu Warszawskiego, 11 – 13.09. 2017 r.]
Opublikowany w: Number Theory Mathods and Cryptography str. 25-36, (LNCS, volume 10737)
Abstract: Elliptic curves over nite elds are an essential part of public key cryptography. The security of cryptosystems with elliptic curves is based on the computational intractability of the Elliptic Curve Discrete Logarithm Problem (ECDLP). The paper presents requirements which cryptographically secure elliptic curves have to satisfy, together with their justication and some relevant examples of elliptic curves. We implemented modular arithmetic in a nite eld, the operations on an elliptic curve and the basic cryptographic protocols.
Keywords: elliptic curve cryptography, modular arithmetic, digital signature ECDSA, Di‑e-Hellman key agreement.