Category: Computer Science

Back in the late 1990s I trained myself in number theory and cryptography using the “Handbook of Applied Cryptography” by Alfred J. Menezes and his coeditors and the FreeLIP (Free Large Integer Package) package by Arjen K. Lenstra. FreeLIP is quite an elegant C library, but it is now considered obsolete. I know of MIRACL that was Henri Cohen’s favorite large integer library. I have four books in my personal library that have unsigned or signed multiple precision integer arithmetic code and/or algorithms: “A Numerical Library in C for Scientists and Engineers” by H .T. Lau, “Handbook of Applied Cryptography”, “Prime Numbers and Computer Methods of Factorization Second Edition” by Hans Riesel, and “Semi-numerical Algorithms Second Edition” by Donald Knuth. I also have several number theory and cryptography textbooks.

As an exercise in Python console programming, I translated my C# Visual Studio 2008 large integer code to Python. Back in 2008 Visual Studio C# did not support large integers. I used Riesel’s input and output code which was translated from Pascal code. I also utilized algorithms from the “Handbook of Applied Cryptography”. I included Sieve of Eratosthenes for primes <= 100,000, a trial division factoring algorithm, and programmed the Pollard rho factoring algorithm found in the handbook.