Abstract: Public data including a prime number p, a natural number d, a matrix Q, and a matrix S are acquired by a public data acquisition section, and secret key including natural numbers nA, kA is generated by a shared secret key generation section. A matrix MA (MA=S?kAQnASkA) is calculated by a non-commutative matrix generation section and transmitted to a communication party, and a matrix MB (MB=S?kBQnBSkB) is acquired from the communication party. A matrix MAB (MAB=S?kAMBnASkA) is computed as a common secret key by a shared secret key computation section. An encryption/decryption device is thereby capable of rapid generation of the secure common secret key.

Abstract: An encryption device generates non-commutative matrices A1, A2 based on private data A and prime numbers p1, p2, and operates the non-commutative matrices A1, A2 on vectors vi1, vi?12. The encryption device performs non-linear transformation to transform the vectors vi1, vi2 into bit sequences, and joins these to the bit sequences W1, W2. The encryption device repeats the operation of the non-convertible matrices and the non-linear transformation until the respective numbers of bits of the bit sequence W1 and the bit sequence W2 have reached a number of bits of a bit sequence expressing encryption target data. The encryption device derives a pseudo-random number bit sequence by computing the exclusive logical sum between the bit sequence W1 and the bit sequence W2, and performs encryption using the pseudo-random number bit sequence.