Аңдатпа
The existing exponentiation-based three-pass cryptographic protocols are not secure against attacks using hypothetic quantum computers. This paper will review the research conducted on the cryptographic security of the three-pass protocol on permutations. An informational message is a permutation 𝜋 of a given length 𝑀. The operations of cryptographic transformation for the proposed protocol are the operations of multiplying permutations, exponentiation of their disjoint cycles, and the operation of finding a conjugate permutation. The steps for implementing the protocol are described in detail. The protocol uses a permutation 𝛼, Alice’s secret key 𝑠, and Bob’s secret keys 𝑟 and 𝜒𝐵 . All disjoint cycles in the permutation 𝜒𝐵 decomposition have different lengths. The length of all 𝛼 disjoint cycles is pairwise coprime with the length of 𝜒𝐵 disjoint cycles. The protocol correctness and single solution are proved. An example of the protocol implementation for 𝑀 = 7 is presented. The Alice’s key space size equals the product of 𝛼 disjoint cycles length. Bob’s key space size equals the product of 𝛼 disjoint cycle length and the number of possible 𝜒𝐵 permutations with a suitable structure. The protocol resistance to some statistical ciphertext-only attacks has been investigated. It is shown that even if the cryptanalyst is informed about the structure of 𝛼 and 𝜒𝐵 cycles, he will not be able to determine permutation 𝜋, neither does this knowledge disclose the keys 𝑠, 𝑟, 𝜒𝐵 values; the cryptanalyst cannot reduce the size of the potential permutation 𝜋 set to a value less than the size of Alice’s key space; even knowing the key 𝜒𝐵 structure and having checked all possible vector 𝑟 values, the cryptanalyst will not be able to determine the key 𝑟; cryptanalyst will not be able to determine the structure of 𝜒𝐵 cycles by going through all possible 𝑟 values. The transformation security is based on the complexity of permutation factorization, as well as on the complexity of implementing transformations that are inverse to nonlinear operations based on the identical cycle structure of conjugate permutations. The protocol keys must be changed after being used. Channel error protection must be provided when implementing the protocol.