| 摘要 |
PROBLEM TO BE SOLVED: To provide a public key ciphering system in which the safety of ciphering is maintained while a normal user easily conducts deciphering. SOLUTION: The symbol Cs represents a matrix of m rows and n columns having two elements '1' in every row, and Cn a reversible matrix of M rows and M columns having two elements '1' in every row. A plain sentence vectorξis multiplied by a matrix Cn-1Cs and a random vectorηin which the appearance probability of '1' is p is added to obtain a ciphered sentence z. Then, the matrix Cn-1Cs and the value p are defined as public keys and the matrices Cn and Cs are defined as secret keys. In order to decode, the ciphered sentence z is multiplied by Cn to obtain a vector b and a parity inspection equation b=CsS+Cnτis defined. Then, the equation is solved with respect to the vectors S andτby using a probabilistic search method such as belief propagation and the estimated value of the sentenceξis obtained as the solution of S.
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