منابع مشابه
Montgomery curves and the Montgomery ladder
The Montgomery ladder is a remarkably simple method of computing scalar multiples of points on a broad class of elliptic curves. This article surveys a wide range of topics related to the Montgomery ladder, both from the historical perspective of Weierstrass curves and from the modern perspective of Edwards curves. New material includes a full proof of a complete constant-time ladder algorithm ...
متن کاملEnhanced Montgomery Multiplication
We define the Non Reduced Montgomery Multiplication of order s, of A and B, modulo N (odd integer) by NRMM(A, B, N) = ( AB + N ( −ABN−1 (mod 2) )) 2−s. Given an upper bound on A and B, with respect to N , we show how to choose the variable s in a way that guarantees that NRMM(A, B, N) < 2N . A few applications are demonstrated, showing the advantage of using NRMM with an appropriately chosen s,...
متن کاملExact Analysis of Montgomery Multiplication
The Montgomery multiplication is often used for an efficient implementations of public-key cryptosystems. This algorithm occasionally needs an extra subtraction in the final step, and the correlation of these subtractions can be considered as an invariant of the algorithm. Some side channel attacks on cryptosystems using Montgomery Multiplication has been proposed applying the correlation estim...
متن کاملLeakage from Montgomery Multiplication
Modular multiplication P = A×B mod M is a fundamental operation in most public key cryptography. Its efficiency is usually critical in determining the overall efficiency of a system because it is the main component in modular exponentiation and in elliptic curve point multiplication. There are several algorithms which can be chosen for performing modular multiplication, of which those by Barret...
متن کاملMontgomery Multiplication in Gf2
We show that the multiplication operation c = a br ,1 in the eld GF2 k can be implemented signiicantly faster in software than the standard multiplication, where r is a special xed element of the eld. This operation is the nite eld analogue of the Montgomery multiplication for modular multiplication of integers. We give the bit-level and word-level algorithms for computing the product, perform ...
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ژورنال
عنوان ژورنال: Acta Dermato-Venereologica
سال: 2003
ISSN: 0001-5555
DOI: 10.1080/00015550410024878