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.