Algorithms for Super Long Integers in Cryptosystems

Super long integers which exceed the limit of numbers defined in existent computers are widely employed in cryptosystems. In the paper, design 10 algorithms which address operands by the byte, and are used for the operation of unsigned super long integers, including conversion between a binary number and a decimal one, shift, comparison, addition, subtraction, multiplication, division, and modular power, analyze the time complexity of each of the algorithms in the amount of bit operations, offer the source code of the modular power operation in C, and give some examples which are utilized for validating the correctness of the algorithms according to the properties of a group.