摘要 |
The present invention relates to a tame automorphism based encryption system or scheme. Let K be a finite field of 2<m> elements. Let phi 4, phi 3, phi 2, phi 1 be tame automorphisms (see above) of the rink K[x1,...,xn+r]. Let the composition be pi = phi 4 phi 3 phi 2 phi 1. The automorphism pi and the factorization pi = phi 4 phi 3 phi 2 phi 1 are hidden. Let pi = ( pi 1(x1,...,xn+r),...,xn+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 phi i<-1>((y'1,...,y'n+r)) (see Corollary 2). Therefore, it is easy to recover the plaintext (x'1,...,x'n) = phi 1<-1> phi 2<-1> phi 3<-1> phi 4<-1> pi (( pi 1,...,x'n)). However without knowing the automorphism pi precisely and the decomposition pi = phi 4 phi 3 phi 2 phi 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.
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