- 81 - Foundations of Cryptography
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چکیده
1. One Way Permutations with Trapdoor We recall the definition of a one-way functions with trapdoor as introduced in lecture 3. We consider a set of one-way permutations {fi:Di→Di} , i∈I⊆{0,1}* where the Di are finite domains, and I is some index set. example: in RSA scheme the functions are { f (N,e):ZN * →ZN }, where N =p .q for primes p,q and e is relatively prime with φ(N). The functions fi satisfy the following requirements: (all algorithms mentioned hereafter are polynomial-time) (1) There exists a sampling algorithm S 1 such that, S 1(1 n) ranges over LI∩{0,1} n M O×{0,1} *
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