Modular multiplication without trial division

@article{Montgomery1985ModularMW,
  title={Modular multiplication without trial division},
  author={Peter L. Montgomery},
  journal={Mathematics of Computation},
  year={1985},
  volume={44},
  pages={519-521}
}
  • P. L. Montgomery
  • Published 1 May 1985
  • Mathematics, Computer Science
  • Mathematics of Computation
Let N > 1. We present a method for multiplying two integers (called N-residues) modulo N while avoiding division by N. N-residues are represented in a nonstandard way, so this method is useful only if several computations are done modulo one N. The addition and subtraction algorithms are unchanged. 1. Description. Some algorithms (1), (2), (4), (5) require extensive modular arith- metic. We propose a representation of residue classes so as to speed modular multiplication without affecting the… 
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