Download Algorithmic Cryptanalysis by Antoine Joux PDF

By Antoine Joux

Illustrating the ability of algorithms, Algorithmic Cryptanalysis describes algorithmic tools with cryptographically proper examples. targeting either inner most- and public-key cryptographic algorithms, it provides each one set of rules both as a textual description, in pseudo-code, or in a C code program.

Divided into 3 components, the e-book starts off with a brief advent to cryptography and a history bankruptcy on trouble-free quantity concept and algebra. It then strikes directly to algorithms, with every one bankruptcy during this part devoted to a unmarried subject and sometimes illustrated with easy cryptographic purposes. the ultimate half addresses extra refined cryptographic functions, together with LFSR-based circulation ciphers and index calculus methods.

Accounting for the influence of present laptop architectures, this ebook explores the algorithmic and implementation facets of cryptanalysis tools. it might probably function a instruction manual of algorithmic tools for cryptographers in addition to a textbook for undergraduate and graduate classes on cryptanalysis and cryptography.

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Example text

In addition, z (p+1)/4 is the only square root of z which is itself a square. When p = 1 (mod 4), matters become more complicated, especially if a large power of 2 divides p − 1. In that case, we need to write p − 1 = 2e q with q odd. The method of choice to compute square roots in this case is Shanks-Tonelli algorithm. This method is based on the remark that for any quadratic residue z = u2 (mod p), the value z (q+1)/2 is “almost” a square e root for z. More precisely, if we let θ = z (q+1)/2 /u, then θ2 = 1.

A relation which is reflexive, symmetric and transitive: • Reflexivity For all pairs (x1 , x2 ), we have (x1 , x2 ) ≡ (x1 , x2 ) since x1 x2 = x1 x2 . • Symmetry For all pairs (x1 , x2 ) and (y1 , y2 ), the equivalence (x1 , x2 ) ≡ (y1 , y2 ) implies (y1 , y2 ) ≡ (x1 , x2 ). • Transitivity For all pairs (x1 , x2 ), (y1 , y2 ) and (z1 , z2 ), if (x1 , x2 ) ≡ (y1 , y2 ) and (y1 , y2 ) ≡ (z1 , z2 ) then (x1 , x2 ) ≡ (z1 , z2 ). Indeed, x1 y2 = y1 x2 implies x1 z2 y2 = y1 x2 z2 and y1 z2 = z1 y2 implies x2 z2 y1 = x2 z1 y2 .

1 Encrypt and MAC Given a secret key encryption scheme and a MAC, the first idea that comes to mind in order to encrypt and protect the integrity of a message M at the same time is simply to concatenate an encryption of M and a MAC of M . The reason that makes this simple idea insecure is that a MAC algorithm does not necessarily hide the complete content of the message. For example, if we are given a secure MAC algorithm, we can easily construct another secure MAC based on it in a way that completely destroys confidentiality.

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