Special issue in honor of Peter Lawrence Montgomery

Excerpt

Peter Lawrence Montgomery was born on September 25, 1947. While an undergraduate at the University of California at Berkeley, he became a Putnam fellow in 1967. Montgomery was one of only two contestants able to solve all twelve problems of that year’s Putnam examination. In April 1992 he received a Ph.D. from the University of California at Los Angeles. In the biography section of his now famous Karatsuba-like paper [7], one can read what Peter Montgomery concisely wrote about himself,

He is best known as the inventor of Montgomery multiplication. He has improved integer factorization algorithms.

In fact, Peter Montgomery is well known for a number of very important contributions in a wide range of topics in computational number theory and cryptography. He is credited with inventing the block version of the Lanczos algorithm, which is useful for finding the kernel of a singular matrix over a finite field [6]. This is a crucial step in the index-calculus procedures used for factorizing large integers and for solving the discrete logarithm problem in finite fields or Jacobian groups. Montgomery was also able to speed up Lenstra’s ECM factorization algorithm by applying fast Fourier transform (FFT) techniques for the rapid evaluation of polynomials [3‐5]. …