Biblio

Development in the area of quantum technologies led to the appearance of first quantum computers. The threat of using a quantum computer for cryptanalysis requires wide implementing post-quantum security in computing algorithms and communication protocols. We evaluate the computational power of some existing quantum computers to illustrate the relevance of research in post-quantum security. One of the best ways to test post-quantum protocols is to embed them into some non-critical but widely-used sphere. Secure messaging is an excellent example of such an application. In the paper, we analyze the post-quantum security of well-known messaging specification Signal, which is considered to have high-security properties. The core of Signal specification is the Double Ratchet protocol. We notice and explain why it is not a post-quantum secure scheme. After that, we suggest some possible ways to improve the security features of Signal specification.

In this paper, we consider ways of organizing group authentication, as well as the features of constructing the isogeny of elliptic curves. The work includes the study of isogeny graphs and their application in postquantum systems. A hierarchical group authentication scheme has been developed using transformations based on the search for isogeny of elliptic curves.