Abstract: A method of creating a secure digital signature, including one or more of the following: a sender, based on a private key K and message x, calculates a unique pair of integers q and r such that int(K)=int(h)q+r, then chooses a cyclic group G with generator g, for which the discrete logarithm problem is a hard problem and computes the public key gint(K), and calculates a pair (gq, gr), which is the digital signature of x, a receiver, who knows a public key gint(K), obtains a message y and a digital signature in a form of pair (gq, gr) and calculates the following two expressions gint(K)(gr)?1 and (gq)int(y), the algorithm generates “TRUE”, if the two expressions match, and “FALSE”, if they do not.

Abstract: Computer software or integrated circuit for performing a secure hashing method including one or more of the following: representing an initial sequence of bits as a specially constructed set of polynomials; transformation of this set by masking; partitioning the transformed set of polynomials into a plurality of classes; forming the bit string during the (separated) partitioning; for each of the plurality of classes, factoring each of the polynomials and so as to define a set of irreducible polynomials and collecting these factors in registers defined for each of the plurality of classes; wrapping the values of the registers from the plurality of classes by means of an enumeration; organizing the enumerations and the bit strings into a knapsack; and performing an exponentiation in a group to obtain the hash value or the MAC value.

Abstract: A system and method of improving the resistance of MAC functions to attack makes use of the output MAC value to perform a one-way operation such as exponentiation in a cyclic group such as a Galois Field. Further enhancements are provided by an optional keyed function that can provide another barrier through which an attacker must break. The application of a keyed function can also be applied to hashing functions so that they have the qualities of a MAC function and additionally benefit from the application of the one way operations to improve security.