Statistical physics of error-correcting codes and public key cryptography

David Saad

The relation between Ising spin systems and public-key cryptography is investigated using methods of statistical physics. The insight gained from the analysis is used for devising a matrix-based cryptosystem whereby the ciphertext comprises products of the original message bits; these are selected by employing two predetermined randomly-constructed sparse matrices. The ciphertext is decrypted using methods of belief-propagation. The analyzed properties of the suggested cryptosystem show robustness against various attacks and competitive performance to modern cyptographical methods.

This work has been done in collaboration with Yoshiyuki Kabashima (TITECH) and Tatsuto Murayama (TITECH). Most of our publications in this area are accessible from our website:, in particular the manuscripts NCRG/2001/008 and NCRG/2000/002.