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Cryptography based on error correcting codes

Publications associées (63)

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Concentration of Magnetization for Linear Block Codes

Nicolas Macris, Satish Babu Korada, Shrinivas Kudekar

We consider communication over the binary erasure and the binary additive white gaussian noise channels using fixed linear block codes and also appropriate ensembles of such codes. We show concentration of the magnetization over the channel realizations an ...

2008

Diversity Embedded Codes: Theory and Practice

Suhas Diggavi, Sanket Dusad

Diversity embedded codes are high-rate space-time codes that have a high-diversity code embedded within them. They allow a form of communication where the high-rate code opportunistically takes advantage of good channel realizations while the embedded high ...

2008

Protection of data from erasures using subsymbol based codes

Mohammad Amin Shokrollahi

An encoder uses output symbol subsymbols to effect or control a tradeoff of computational effort and overhead efficiency to, for example, greatly reduce computational effort for the cost of a small amount of overhead efficiency. An encoder reads an ordered ...

2008

A family of non-binary TLDPC codes: density evolution, convergence and thresholds

We generalize the results about how to compute iterative decoding thresholds over the binary erasure channel of non-binary LDPC code ensembles of [16] to non-binary TLDPC codes [2], [3]. We show in this case how density evolution can be performed in order ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2007

TCHo: a Hardware-Oriented Trapdoor Cipher

Serge Vaudenay, Willi Meier, Jean-Philippe Aumasson

This paper improves the Finiasz-Vaudenay construction of TCHo, a hardware-oriented public-key cryptosystem, whose security relies in the hardness of finding a low-weight multiple of a given polynomial, and on the decoding of certain noisy cyclic linear cod ...

Springer2007

Good Ensembles of Goppa Codes

Ghid Maatouk

It is well-known that random error-correcting codes achieve the Gilbert-Varshamov bound with high probability. In [2], the authors describe a construction which can be used to yield a polynomially large family of codes of which a large fraction achieve the ...

2007

Griffiths Kelly Sherman correlation inequalities: a useful tool in the theory of error correcting codes

Nicolas Macris

It is shown that a correlation inequality of statistical mechanics can be applied to linear low-density parity-check codes. Thanks to this tool we prove that, under a natural assumption, the exponential growth rate of regular low-density parity-check (LDPC ...

Institute of Electrical and Electronics Engineers2007

Systems and processes for fast encoding of hamming codes

Mohammad Amin Shokrollahi

Decoding that uses an extended Hamming code in one of the primary stages of static encoding uses a calculation of the r+1 Hamming redundant symbols for k input symbols from which Hamming redundant symbols are calculated, where r satisfies 2.sup.r-1-r.ltore ...

2007

Cryptanalysis of the Sidelnikov cryptosystem

Mohammad Amin Shokrollahi, Lorenz Minder

We present a structural attack against the Sidelnikov cryptosystem. The attack creats a private key from a give public key. Its running time is subexponential and it is effective if the parameters of the Reed-Muller code allow for efficient sampling of min ...

Springer Verlag2007

Computational Hardness and Explicit Constructions of Error Correcting Codes

Mohammad Amin Shokrollahi, Mahdi Cheraghchi Bashi Astaneh

We outline a procedure for using pseudorandom generators to construct binary codes with good properties, assuming the existence of sufficiently hard functions. Specifically, we give a polynomial time algorithm, which for every integers

n

and

k

, constru ...

2006

Computational Hardness and Explicit Constructions of Error Correcting Codes

Mohammad Amin Shokrollahi, Mahdi Cheraghchi Bashi Astaneh

n

and

k

, constru ...

2006