Software complex for fast multiplication and exponentiation over large modules using minimally redundant modular Montgomery scheme for cryptosystems

Original interval-index technology of modular code expansion surpasses known analogs in speed and the number of required tables in k/2 times (k-total number of bases). The use of a 16-bit rather than 32-bit MSS bases enables the widespread introduction of table-summatory configurations of computational procedures.

This basic mathematic software for cryptosystems of modular type allows to use working modules of almost any capacity. At 1024*2462-bit capacity of a PC with a frequency of 2.27 GHz:
• modulo multiplication task takes from 0.6 to 3.6 ms
• modulo exponentiation task takes from 0.3 to 8.3 sec
• RAM memory space for working set of tables is 153-362 MB.
• the process of tables generation is realized as a preliminary and does not exceed 0.3 and 0.7 sec at 1024- and 2462-bit p, respectively.

In comparison with the software version of the best modular development (brand Toshiba) and adequate analogue based on positional arithmetic the performance improves approximately in 2 and 5 times, respectively. Three-fold or four-fold gain in performance in comparison with modular analogues is achieved on a computer-arithmetic level without any expensive hardware, which provides a significant reduction in development costs.
Cryptosystems software is easy-to-operate and does not require any specialized knowledge.

Information security, Informatics

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