Cryptography

Download Cryptography and Coding: 14th IMA International Conference, by Sihem Mesnager (auth.), Martijn Stam (eds.) PDF

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By Sihem Mesnager (auth.), Martijn Stam (eds.)

This ebook constitutes the court cases of the 14th IMA overseas convention on Cryptography and Coding, IMACC 2013, held at Oxford, united kingdom, in December 2013. The 20 papers offered have been rigorously reviewed and chosen for inclusion during this e-book. they're geared up in topical sections named: bits and booleans; homomorphic encryption; codes and purposes; cryptanalysis; retaining opposed to leakage; hash capabilities; key matters and public key primitives.

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Additional resources for Cryptography and Coding: 14th IMA International Conference, IMACC 2013, Oxford, UK, December 17-19, 2013. Proceedings

Example text

A state A is organized as an array of 5 × 5 lanes each of length w ∈ {1, 2, 4, 8, 16, 32, 64}. e. b ∈ {25, 50, 100, 200, 400, 800, 1600}. The number of rounds nr depends on the state size and is given by nr = 12+2 where = log2 w. A round consists of a sequence of invertible steps on the state A[x][y][z]: – θ step is a linear map and can be divided into three steps: C[x] = A[x, 0] ⊕ A[x, 1] ⊕ A[x, 2] ⊕ A[x, 3] ⊕ A[x, 4] for x = 0, . . , 4 D[x] = C[x − 1] ⊕ (C[x + 1] ≫ 1) for x = 0, . . , 4 A[x, y] = A[x, y] ⊕ D[x] for x, y = 0, .

Q − 1. Note that if we start from an irreducible non-primitive polynomial g of degree n and order d and construct the finite field F2n as the algebraic extension by β, a root of g, then there are several primitive elements α ∈ F2n which are solutions for β = αq (with q = (2n − 1)/d). Moreover these α need not all have the same minimal polynomial. 22 D. Gardner, A. -W. Phan Our goal is, given g, to produce one elementary sequence from each of the q equivalence classes; moreover these sequences should be in the correct phase relative to each other (as described by Theorem 4) such that they may be interleaved to generate an m-sequence.

It follows that a plaintext can be viewed as a vector of elements in GF(2d ) and vice-versa. Moreover, arithmetic over plaintexts correspond to element-wise arithmetic over -vectors. Elements of this -vector are usually referred to as slots. In [13] it is shown how to move the content of a slot in another one, using automorphisms over R2 . Recall that for any i ∈ Z∗m the automorphism κi over R2 is defined as κi : a(x) → a(xi ) (mod Φm (x)). Up to a reordering of factors Fi , there exists an integer h such that if a ∈ R encodes the -vector (a0 , .

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