Abstract: 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≡Me (mod n) using a first secret key given by N (≧2) prime numbers p1, p2, . . . , pN, a first public key n given by a product p1k1 p2k2 . . . pNkN where k1, k2, . . . , kN are arbitrary positive integers, a second public key e 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 Mp1k1, Mp2k2, . . . , MpNkN modulo p1k1, p2k2, . . . , pNkN, respectively, of the plaintext M using a prescribed loop calculation with respect to the first secret key p1, p2, . . . , pN, and by applying the Chinese remainder theorem to the residues Mp1k1, Mp2k2, . . . , MpNkN. This encryption/decryption scheme can be utilized for realizing the authentication.

Abstract: A secret communication and authentication scheme based on a public key cryptosystem in which a decryption speed is improved while maintaining a security level. In the RSA type secret communication, a plaintext is expressed in a form of a k-digit base n number and a ciphertext is obtained by applying a calculation using the first public key n and the second public key e to the base n number and transmitted. Then, from the received ciphertext, a lowest digit of the base n number is decrypted by using the first public key n and the second secret key d, upper digits of the base n number are sequentially decrypted by using a decrypted value of the lowest digit of the base n number at the receiver side, and the plaintext is recovered by using decrypted values of respective digits of the base n number. The Rabin type secret communication can also be realized by the similar scheme.

Abstract: A carrier comprising a ceramic substrate, an active alumina coating formed thereon and at least one sinter inhibitor such as Mg dispersed in the active alumina-coated substrate, the carrier having excellent heat resistance and great thermal shock resistance and enabling a catalyst to be carried thereon to keep its catalytic activity substantially invariable even at high temperatures.