1985/01/01 by Peter L. Montgomery · 1 citation
Computer Science · #Cryptography and Residue Arithmetic #Numerical Methods and Algorithms #Coding theory and cryptography
paper · doi:10.1090/s0025-5718-1985-0777282-x
openalex publication_date 1985/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper N greater-than 1"> <mml:semantics> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>></mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">N > 1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> . We present a method for multiplying two integers (called <italic>N-residues</italic> ) modulo <italic>N</italic> while avoiding division by <italic>N</italic> . <italic>N</italic> -residues are represented in a nonstandard way, so this method is useful only if several computations are done modulo one <italic>N</italic> . The addition and subtraction algorithms are unchanged.