Paper 2014/214

Squaring Algorithms with Delayed Carry Method and Efficient Parallelization

Vladislav Kovtun and Andrew Okhrimenko

Abstract

Increasing amounts of information that needs to be protecting put in claims specific requirements for information security systems. The main goal of this paper is to find ways to increase performance of cryptographic transformation with public key by increasing performance of integers squaring. Authors use delayed carry mechanism and approaches of effective parallelization for Comba multiplication algorithm, which was previously proposing by authors. They use the idea of carries accumulation by addition products of multiplying the relevant machine words in columns. As a result, it became possible to perform addition of such products in the column independently of each other. However, independent accumulation of products and carries require correction of the intermediate results to account for the accumulated carries. Due to the independence of accumulation in the columns, it became possible to parallelize the process of products accumulation that allowed formulating several approaches. In this paper received theoretical estimates of the computational complexity for proposed squaring algorithms. Software implementations of algorithms in C++ allowed receiving practical results of the performance, which are not contrary to theoretical estimates. The authors first proposed applying the method of delayed carry and parallelization techniques for squaring algorithms, which was previously proposing for integer multiplication.