1. A method of cryptographically hashing a message M, comprising the steps of: forming a sequence (M 1 ,. .. , Mi,. .. , Mc) of data m-tuples M 1 =(a 1,1,. .. , a 1,m ),. .. , Mi=(a i,1 ,. .. , a i,m ),. .. , Mc=a c,1 ,. .. , a c,m ), where m is a strictly positive integer, from said message M; iteratively calculating successive output p-tuples (V 1 ,. .. , V i ,. .. , V c ), where p is a strictly positive integer, corresponding to said sequence (M 1 ,. .. , Mi,. .. , Mc) of data m-tuples as a function of at least one set of multivariate polynomials defined over a finite field, said iterative calculation of the successive output p-tuples (V 1 ,. .. , V i ,. .. V c ) including the steps of: defining an initialization input p-tuple E 0 =(e 01 ,. .. , e 0p ) in the finite field; applying said initialization input p-tuple E 0 and a first data m-tuple M 1 to said at least one set of multivariate polynomials to calculate a first output p-tuple V 1 corresponding to said first data m-tuple M 1 ; in each new current iteration i, defining a current input p-tuple E i =(e i1 ,. .. , e ip ) in the finite field that is a function at least of one of the output p-tuples (V 1 ,. .. , V i-1 ) calculated in the preceding iterations, and applying said current input p-tuple Es and a current data m-tuple Mi to said at least one set of multivariate polynomials to calculate a current output p-tuple V i corresponding to said current data m-tuple Mi; and determining a hashing value of said message M as a function of the last output p-tuple V c .