Public key cryptography and error correcting codes as Ising models

Details Public key cryptography and error correcting codes as Ising models Public key cryptography and error correcting codes as Ising models

2000-08-24

arxiv.org/abs/cond-mat/0008363v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

6 pages

Scientific paper

10.1063/1.1358168

We employ the methods of statistical physics to study the performance of Gallager type error-correcting codes. In this approach, the transmitted codeword comprises Boolean sums of the original message bits selected by two randomly-constructed sparse matrices. We show that a broad range of these codes potentially saturate Shannon's bound but are limited due to the decoding dynamics used. Other codes show sub-optimal performance but are not restricted by the decoding dynamics. We show how these codes may also be employed as a practical public-key cryptosystem and are of competitive performance to modern cyptographical methods.

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