| 摘要 |
A new scheme for fast realization of encryption, decryption and authentication which can overcome the problems of the RSA cryptosystem is disclosed. The encryption obtains a ciphertext C from a plaintext M according to C ~ M e (mod n) using a first secret key given by N (~ 2) prime numbers p1, p2, ~, p N, a first public key n given by a product p1 k1p2 k2 ~ p N kN where k1, k2, ~, kN are arbitrary positive integers, a second public key a and a second secret key d which satisfy ed ~ 1 (mod L) where L is a least common multiple of p1-1, p2-1, ~, pN-1. The decryption recovers the plaintext M by obtaining residues M p1k1, M p2k2, ~, M pNkN modulo p1k1, p2k2, ~, p NkN, respectively, of the plaintext M using a prescribed loop calculation with respect to the first secret key p1, p2, ~, p N, and by applying the Chinese remainder theorem to the residues M p1k1, M p2k2, ~, M pNkN. This encryption/decryption scheme can be utilized for realizing the authentication.
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