Arithmetic, Geometry, Cryptography and Coding Theory 2009 by David Kohel, Robert Rolland (ed.)

By David Kohel, Robert Rolland (ed.)

Show description

Read or Download Arithmetic, Geometry, Cryptography and Coding Theory 2009 PDF

Best popular & elementary books

Numerical embedded computing

Mathematical algorithms are crucial for all meeting language and embedded approach engineers who strengthen software program for microprocessors. This booklet describes thoughts for constructing mathematical exercises - from basic multibyte multiplication to discovering roots to a Taylor sequence. All resource code is on the market on disk in MS/PC-DOS layout.

Morse Theory

Probably the most stated books in arithmetic, John Milnor's exposition of Morse thought has been crucial ebook at the topic for greater than 40 years. Morse idea used to be built within the Nineteen Twenties by way of mathematician Marston Morse. (Morse used to be at the college of the Institute for complex research, and Princeton released his Topological equipment within the idea of capabilities of a fancy Variable within the Annals of arithmetic reports sequence in 1947.

A History of the mathematical theory of probability from the time of Pascal to that of Laplace

It is a copy of a e-book released prior to 1923. This publication can have occasional imperfections reminiscent of lacking or blurred pages, bad images, errant marks, and so on. that have been both a part of the unique artifact, or have been brought by way of the scanning technique. We think this paintings is culturally very important, and regardless of the imperfections, have elected to deliver it again into print as a part of our carrying on with dedication to the protection of revealed works around the world.

Extra resources for Arithmetic, Geometry, Cryptography and Coding Theory 2009

Example text

Moreover, if v divides each of these two factors then in fact v | r. We are then led to consider two cases. First, suppose that v r. Then either v 2 | (t1 + t2 ) or v 2 | (r + t1 + t2 ). Let h = (g + 1)/2 . If m = deg v ≤ h, then by sieving we conclude that v 2 | pt for at most 2q g+1−2m+1 = 2q g+2−2m values of t. On the other hand, if m > h then deg v 2 > g + 1 so by sieving we now have v | pt for at most two values of t. Since the number of monic irreducible polynomials of degree m over k is bounded by q m /m, the number of values of t such that pt is 24 4 WOUTER CASTRYCK AND JOHN VOIGHT divisible by v 2 with v r is at most q g+1 q2 qh q h+1 (2q g+2−4 ) + · · · + (2q g+2−2h ) + 2 + ···+ 2 2 h h+1 g+1 g g+2−h h+1 g+1 q q q q + ···+ + + ··· + = 2 q g+1 + 2 h h+1 g+1 q(2q g+2−2 ) + = ≤ ≤ 2+ 2 g+1 h q g+1 + 2 i=2 q g+2−i + i q g+1 − 1 2 q g+1 + 2 2+ g+1 q−1 2 2 + q g+1 .

By repeating this technique, he can recover the secret scalar. This type of fault injection is also called computational safe-error attack. However, for the Montgomery ladder, the situation is different as every intermediate result is used to compute the final result. Hence, if the attacker induces a fault the final result will inevitably be corrupted. Joye and Yen [JY02] proposed a slight modification to the Montgomery ladder in order to make it resistant to M safe-error attacks, an attack that implies stronger assumptions in the attacker’s capabilities.

Each elliptic curve operation is implemented as the repetition of blocks of instructions that look alike in the power trace. The code of the scalar multiplication algorithm is then unrolled such that it appears as a repetition of the same atomic block. The sequence of blocks does not depend on the scalar used and their algorithm is then secure against SPA. A doubling in Jacobian coordinates is computed using 10 atomic blocks and 16 blocks for an addition, each atomic block costing 1M . However their construction uses dummy operations and can then be sensitive to fault attacks.

Download PDF sample

Rated 4.45 of 5 – based on 23 votes