Handbook of elliptic and hyperelliptic curve cryptography amazon

Create Alert Alert. Share This Paper. Background Citations. Methods Citations. Results Citations. Topics from this paper.

Hyperelliptic curve cryptography Smart card Public-key cryptography. Computation Pairing-based cryptography Primality test. Integer factorization Descent. Citation Type. Has PDF. Publication Type. More Filters. Many modern computer systems include — beside a CPU — such a powerful GPU which runs idle most of the time and might be used as cheap and instantly available co-processor for general purpose applications.

In this contribution, we focus on the efficient realisation of the computationally expensive operations in asymmetric cryptosystems on such off-the-shelf GPUs. Moreover, our design for ECC over the prime field P even achieves the throughput of point multiplications per second.

In this paper, we propose a efficient and secure point multiplication algorithm, based on double-base chains. This is achieved by taking advantage of the sparseness and the ternary nature of the socalled double-base number system DBNS. The speed-ups are the results of fewer point additio Our algorithms can be protected against simple and differential side-channel analysis by using side-channel atomicity and classical randomization techniques.

Our numerical experiments show that our approach leads to speed-ups compared to windowing methods, even with window size equal to 4, and other SCA resistant algorithms. Sutherland , We present a space-efficient algorithm to compute the Hilbert class polynomial HD X modulo a positive integer P, based on an explicit form of the Chinese Remainder Theorem. We describe practical optimizations that allow us to handle larger discriminants than other methods, with D as large as and h D up to We apply these results to construct pairing-friendly elliptic curves of prime order, using the CM method.

Kohel , On an elliptic curve, the degree of an isogeny corresponds essentially to the degrees of the polynomial expressions involved in its application.

Abstract - Cited by 27 2 self - Add to MetaCart On an elliptic curve, the degree of an isogeny corresponds essentially to the degrees of the polynomial expressions involved in its application. In most algorithms involving elliptic and hyperelliptic curves, the costliest part consists in computing multiples of ideal classes.

The full version can be found in section Sample Chapter. Preface 1. Algebraic Background was online June 01 - July 01, 3. Background on p-adic Numbers was online September 29 - November 3, 4. Background on Curves and Jacobians was online June 6 - July 6, 5. Background on Pairings was online April 22 - June 5, 7. Background on Weil Descent was online September 17, 8. Exponentiation currently online Integer Arithmetic was online January 8 - February 14, Finite Field Arithmetic was online February 12 - March 13, Arithmetic of Elliptic Curves was online September 10 - October 22, Arithmetic of Hyperelliptic Curves was online December 20, - May 31, Arithmetic of Special Curves was online February 14 - March 18,