First, the author describes in detail the construction of modular elliptic curves, giving an explicit algorithm for their computation using modular symbols. Secondly a collection of algorithms for the arithmetic
Algorithms for Modular Elliptic Curves by J. E. Cremona Publisher: Cambridge University Press 1992ISBN/ASIN: 0521418135ISBN-13: 9780521418133Number of pages: 351 Description:Elliptic curves are of central importance in computational number theory with numerous applications in such areas as cryptography ...
Although the idea of using modular symbols for computing the modular elliptic curves defined over Q with conductor N is not new, neither the complete description of the algorithm nor the description of its implementation had been available before the writing of this book; moreover, the complete ...
Describes in detail an algorithm based on modular symbols for computing modular elliptic curves. Also describes various algorithms for studying the arithmetic of elliptic curves.
Elliptic Curves Signature Schemes Zero Knowledge ProofsWe introduce in this paper the algorithmic aspect of elliptic curves together with their applications. We also recall one of the promising application in the field of zero knowledge proofs with concrete implementations....
Summation polynomial algorithms for elliptic curves in characteristic two. In Progress in Cryptology - INDOCRYPT 2014, volume 8885 of LNCS, pages 409-427, 2014.Galbraith S.D., Gebregiyorgis S.W.: Summation polynomial algorithms for elliptic curves in character- istic two. In: Meier W., ...
Data files containing the Cremona Database of all elliptic curves over Q of bounded conductor: see also http://www.lmfdb.org/EllipticCurve/Q . For a description of how most of the data here was computed, see the ANTS 7 Proceedings at http://www.math.tu-berlin.de/~kant/ants/proceedings...
Our results demonstrate that laddering implementations can be competitive with window-based methods by obtaining a new speed record for laddering implementations of elliptic curves on high-end Intel processors.doi:10.1007/978-3-319-71501-8_5Diego F. Aranha...
Generics introduce significant performance overhead and are not yet suited for high performance computing. To regenerate the files, see internal/generator/main.go. Run: go generate ./... Benchmarks Benchmarking pairing-friendly elliptic curves libraries The libraries are implemented in different ...
Java Card compliant cryptographic library for encryption and decryption of RSA, DSA, Diffie-Hellman, El-Gamal and Elliptic Curves algorithms The Public Key Cryptographic Library (PKCL) provides standardized key computation, encryption, decryptio...