Shamus Software Limited

Other Features

Many public key cryptographic algorithms depend on the difficulty of integer factorisation, or the discrete logarithm problem. MIRACL contains two sample programs for calculating discrete logarithms, and implementations of all modern methods of integer factorisation (brute force, Pollard Rho, P-1, P+1, elliptic curve and multiple polynomial quadratic sieve). A Windows 95/NT DOS executable which factors integers using one or more of these techniques can be found in factor.exe. This program is placed into the public domain. The latest version factors all numbers up to 80 digits in length.

As well as multiprecision integers, MIRACL supports fixed-length multiprecision rational numbers in so-called floating slash form. Floating slash (Flash) variables are stored as numerator and denominator - in fact as a fraction. It is not widely known that fractions can be rounded down to a fixed length, but they can, using mediant rounding. More details can be found in the MIRACL manual.

To get a feel for Flash arithmetic, and its almost magical ability to get the right answer, download and try out the public domain DOS executable ratcalc.exe, which implements a full-featured scientific calculator, accurate to 36 places.