Isogeny-Based Cryptographic Access Control

Cryptographic access control is a relatively new concept that implements the access control rules of some subjects to an object using cryptographic primitives. A quantum computer of sufficient capacity allows solving in polynomial time the discrete logarithm and integer factorization problems, which are the basis of most modern public-key cryptosystems. In this regard, there is a need to search for new problems that are resistant to attacks on both classical computers and quantum computers. Computing the isogenies of supersingular elliptic curves is one of the most challenging problems. A scheme for cryptographic access control based on isogenies is proposed. Security analysis of the protocol and the results of practical implementation in the SAGE computer algebra system are given.