A method for reducing a value a to a reduction of the value modulo a modulus p, said modulus p being a prime represented by a data string having a length of g words, said method comprising: - representing (42, 342) the value a as an ordered sequence of f words, where f is greater than g, said sequence thereby including ( f- g) lower order words, each of said words of said sequence having a predetermined number of computer readable bits arranged in a bit pattern to represent a value of that word; - eliminating (45, 345) said ( f- g) lower order words of said sequence so that not more than g words remain in said sequence by, for each of said lower order words, performing successive substitutions (44, 344) in said sequence of an equivalent value, modulo p; said equivalent value being represented by at least one word, each such word having an order higher than that of said lower order word for which such equivalent value is substituted; said successive substitutions (44, 344) being absent a multiplication operation step and applying a bit pattern representing said lower order word in said sequence to higher order words to provide said equivalent value; each substitution of said successive substitutions (44, 344) successively eliminating (45, 345) each said lower order word at each iteration to result in higher order words remaining in said sequence; wherein each substitution (44, 344) includes a summation of like-order words and attribution of a borrow to an adjacent word of higher order when said summation produces a value less than a minimum word value and a carry to an adjacent word of higher order when said summation produces a value greater than a maximum word value; - propagating (48, 348), said carries and said borrows arising during said summation of said equivalent values and performing (51,52; 351,352) further reduction to maintain not more than g words in said sequence; and - utilizing, the ordered sequence of g words remaining as a representation of the reduction of the value modulo p, wherein said equivalent value includes a negative higher order word. - representing (42, 342) the value a as an ordered sequence of f words, where f is greater than g, said sequence thereby including ( f- g) lower order words, each of said words of said sequence having a predetermined number of computer readable bits arranged in a bit pattern to represent a value of that word; - eliminating (45, 345) said ( f- g) lower order words of said sequence so that not more than g words remain in said sequence by, for each of said lower order words, performing successive substitutions (44, 344) in said sequence of an equivalent value, modulo p; said equivalent value being represented by at least one word, each such word having an order higher than that of said lower order word for which such equivalent value is substituted; said successive substitutions (44, 344) being absent a multiplication operation step and applying a bit pattern representing said lower order word in said sequence to higher order words to provide said equivalent value; each substitution of said successive substitutions (44, 344) successively eliminating (45, 345) each said lower order word at each iteration to result in higher order words remaining in said sequence; wherein each substitution (44, 344) includes a summation of like-order words and attribution of a borrow to an adjacent word of higher order when said summation produces a value less than a minimum word value and a carry to an adjacent word of higher order when said summation produces a value greater than a maximum word value; - propagating (48, 348), said carries and said borrows arising during said summation of said equivalent values and performing (51,52; 351,352) further reduction to maintain not more than g words in said sequence; and - utilizing, the ordered sequence of g words remaining as a representation of the reduction of the value modulo p,