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

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

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

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

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Then, we give the smaller value of m which satisfies our conditions, together with the degree of Φm and its lower bound N . Then, the dimension of the larger modulo of the scheme qL−1 is provided. In the last columns, we give execution time and ciphertexts size. The ciphertext size is estimated according to the formula: 2 · ϕ(m) · log2 qL−1 . Both implementations require a number of levels equal to 40. For the packed implementation we need to set m larger than for the byte-sliced implementation, because we need at least sixteen slots per cipherext.

The different cyclic shifts of a sequence are sometimes called “phases”, especially in engineering contexts. Shifting relates to the Seq() notation as follows: Lemma 1. Let b, b1 , b2 ∈ F∗2n , and h ∈ Z. (Seqβ (b) h) = Seqβ (bβ −h ) (Seqβ (b) (Seqβ (b1 ) h) = Seqβ (bβ h ) h) = Seqβ (b2 ) ⇔ h = logβ (b1 b−1 2 ). Proof. The proof is similar to [7, Lemma 1], as it does not depend on whether the minimal polynomial of β is primitive or not. 3 Fibonacci and Galois LFSRs We recall the definition of both the Fibonacci and Galois Linear Feedback Shift Registers (LFSRs) and establish the notations that we will use later.

An−1 is a basis of F2n (viewed as an n-dimensional vector space over F2 ) if and only if Seqβ (a0 ), Seqβ (a1 ), . . , Seqβ (an−1 ) is a basis of the set of sequences with minimal polynomial g (viewed as an n-dimensional vector space over F2 ). Proof. Let a ∈ F2n . a0 , a1 , . . , an−1 is a basis of F2n iff there are unique n−1 c0 , c1 , . . , cn−1 ∈ F2 such that a = i=0 ci ai iff there are unique n−1 c0 , c1 , . . , cn−1 ∈ F2 such that Seqβ (a) = Seqβ ( n−1 i=0 ci ai ) = i=0 ci Seqβ (ai ) iff Seqβ (a0 ), Seqβ (a1 ), .

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