Development of kleptographic mechanisms into hash functions

This research belongs to kleptographic problems of hash functions. Relevance of the research follows from importance of hash functions in hybrid cryptosystem and also from existence of kleptographic attack vectors on such systems. Currently, there are numerous results at kleptography in symmetric ciphers and asymmetric crypto protocols which demonstrate different aspects of kleptographic trapdoor implementation, however, a few of them highlight kleptographic problems of hash functions. Insufficiency of researches in hash kleptography problems leads to kleptography related risks in hash function at designing and standardization stage. In this article, we analyse ways to develop hash functions with kleptographic trapdoor. One of informal requirements for such functions is ''proximity'' to famous and common used constructions, i.e. it must be based on common schemes, that are used for development of well known hash functions. In current paper, it's suggested to build trapdoored hash function based on Merkle-Damgard scheme, which is the base of numerous of wide spread hash function. As compression function we choose one of the well known compression function schemes which are based on block ciphers and are proved to be collision resistant (like as Davice-Mayer or Miyaguchi-Preneel constructions). Instead of block ciphers in compression function we use special transformation based of Discrete Logarithm Problem and prove collision resistance preserving. The final result of the research is hash function with kleptographic trapdoor which allows developer effectively recover part of message (till 50\%) using knowledge of hash digest and secret in the kleptographi trapdoor design. In the same time, this function is still secure for other users who don't own design's secret