Algebraic Informatics: 5th International Conference, CAI by Gul Agha (auth.), Traian Muntean, Dimitrios Poulakis, Robert

By Gul Agha (auth.), Traian Muntean, Dimitrios Poulakis, Robert Rolland (eds.)

This publication constitutes the refereed court cases of the fifth overseas convention on Algebraic Informatics, CAI 2013, held in Porquerolles, France in September 2013. the nineteen revised complete papers awarded including five invited articles have been rigorously reviewed and chosen from a variety of submissions. The papers conceal themes resembling facts types and coding idea; basic elements of cryptography and protection; algebraic and stochastic versions of computing; good judgment and software modelling.

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Extra info for Algebraic Informatics: 5th International Conference, CAI 2013, Porquerolles, France, September 3-6, 2013. Proceedings

Example text

Steganography 1 Introduction Steganography (from greek steganos, or “covered”, and graphie, or “writing”) is the art and science of hidding a secret message within an ordinary message (the cover-medium) in such a way that no one, apart from the sender and intended recipient, even realizes there is a hidden message. While cryptography intends to make a message unreadable from a third party without hiding the secret communication, the aim of steganography is covert communication to hide the message from a third party.

This way, the public matrix can only be described from the first line of the random matrix which in particular decreases the size of the data which must be stored by the prover. The underlying difficult problem upon which the security of the scheme is linked can be stated as follows: Name Input : Syndrome Decoding of Double Circulant Linear Codes : H(k, 2k) a double binary circulant matrix , s a binary column vector with r coordinates, p an integer. Question : Is there a binary vector e of length n such that H te = s and w(e) ≤ p ?

Let n = 2m , it seems that for irreducible Goppa codes the dimension k always satisfies k = n − mt, hence t = (n − k)/ log2 (n). The underlying problem to solve is then the following: Name : GPBD (Goppa Parametrized Bounded Decoding) Input : G a fullrank binary matrix k × n , y ∈ {0, 1}n Question : Does there exists e ∈ {0, 1}n such that y + e be a linear combination of rows from G and w(e) (n − k)/ log2 n ? This problem is NP-complete [43]. 2 binary operations using the algorithms to solve the SD problem [26].

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