Production took place in Sydney for the movie Australia (2008 film).
In modular arithmetic computation , Montgomery modular multiplication , more commonly referred to as Montgomery multiplication , is a method for performing fast modular multiplication .. modular arithmetic. modular arithmetic. It was introduced in 1985 by the American mathematician Peter L. Montgomery .. Peter L. Montgomery. Peter Montgomery ( mathematician ). Given two integers and and module , the classical modular multiplication algorithm computes .. Montgomery multiplication works by transforming and into a representation known as Montgomery form .. For a modulus , the Montgomery form of is defined to be for some constant depending only on and the underlying computer architecture .. If and are the Montgomery forms of and , then their Montgomery product is .. Montgomery multiplication is a fast algorithm to compute the Montgomery product .. Transforming the result out of Montgomery form yields the classical modular product .. Because of the overhead involved in converting and into Montgomery form , computing a single product by Montgomery multiplication is slower than computing the product in the integers and performing a modular reduction by division or Barrett reduction .. Barrett reduction. Barrett reduction. However , when many products are required , as in modular exponentiation , the conversion to Montgomery form becomes a negligible fraction of the time of the computation , and performing the computation by Montgomery multiplication is faster than the available alternatives .. modular exponentiation. modular exponentiation. Many important cryptosystems such as RSA and Diffie -- Hellman key exchange are based on arithmetic operations modulo a large number , and for these cryptosystems , the increased speed afforded by Montgomery multiplication can be important in practice .. RSA. RSA ( cryptosystem )