| 摘要 |
The cryptographic system comprises at least one encryption station, one decryption station and a trapdoor generator. The trapdoor generator comprises means for selecting r distinct prime numbers p @ , generating a modulus m that is a product of the prime numbers p @ , selecting a pair of integers (a,b) satisfying 0 </= a < m and 0 </= b < m, computing for each p @ a number N(p @ ) of distinct pairs of integers (x,y) satisfying 0 </= x < p @ and 0 </= y < p @ and y<2> IDENTICAL x<3> + a.x + b (mod p @ ) and a sum N(p @ ) + 1 representative of an order of an elliptic curve defined as the set of pairs of integers (x,y), computing a least common multiple mu of the values N(p @ ) + 1, selecting a public multiplier e relatively prime to mu , computing a secret multiplier d according to d IDENTICAL 1/e (mod mu ), and transferring data comprising at least m, a, b and e to a storage means provided in the cryptographic system. Alternatively, the trapdoor generator comprises means for selecting r distinct prime numbers p @ each corresponding to a sum value (p @ + 1) that satisfies (p @ + 1) IDENTICAL 0 (mod j) wherein 1 </= @ </= r and j is 3 or 4, generating a modulus m that is a product of the prime numbers p @ , computing the least common multiple mu of the numbers (p @ + 1), selecting a public multiplier e relatively prime to mu , computing a secret multiplier d according to d IDENTICAL 1/e (mod mu ), and transferring data comprising at least m and e to a corresponding storage means provided in the cryptographic system. <IMAGE> |
