| 摘要 |
The present invention relates to a tame automorphism based encryption system or scheme. Let K be a finite field of 2m elements. Let +526 4,+526 3,+526 2, +526 1 be tame automorphisms (see above) of the ring K[x1, . . . ,xn+r]. Let the composition be pi =+526 4+526 3+526 2+526 1. The automorphism pi and the factorization pi =+526 4+526 3+526 2+526 1 are hidden. Let pi =( pi 1(x1, . . . ,xn+r), . . . , pi n+r(x1, . . . , xn+r)). The field K and the polynomials (f1, . . . , fn+r)=( pi 1(x1, . . . ,xn, 0, . . . ,0), . . . , pi n+r (x1, . . . ,xn,0, . . . ,0)) will be announced publicly. Let (x'1, . . . ,x'n) be the plaintext. Then the cyphertext will be (y'1, . . . ,y'n+r)=(f1(x'1, . . . ,x'n), . . . , fn+r(x'1, . . . ,x'n)). It is easy to find +526 i-1((y'1, . . . , y'n+r)) (see Corollary 2). Therefore, it is easy to recover the plaintext (x'1, . . . ,x'n)=+526 1-1+526 2-1+526 3-1+526 4-1 pi (( pi 1, . . . ,x'n)). However without knowing the automorphism pi precisely and the decomposition pi =+526 4+526 3+526 2+526 1, it is very hard to find plaintext (x'1, . . . ,x'n). The encryption system or scheme may be applied to electronic message transmission, data storage, smart card security, and product verification applications. |
