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Public key cryptography and error correcting codes as Ising models

David Saad·Yoshiyuki Kabashima·Tatsuto Murayama
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Abstract

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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David Saad, Yoshiyuki Kabashima, Tatsuto Murayama. 2000-08-24. Public key cryptography and error correcting codes as Ising models. https://doi.org/10.1063/1.1358168

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