The paper is dedicated to construction of new fast and flexible hash-based message authentication codes (HMACs) that will provide large files with cryptographically stable digestions in the Postquantum era. These instruments can be used for detecting cyber-terrorist attacks, file audits and checking the integrity of messages during communication, We use algebraic properties of well known extremal graphs D(n, q) and A(n,q) with good expansion property for the construction of HMACS.
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