Operation of Super Long Integers in Cryptographic Applications

Super long integers which are outside the confines of numbers defined in existent program language compilers or interpreters are widely employed in cryptographic applications. The paper designs 10 algorithms, which almost all address operands by the byte, and are used for the operation of unsigned super long integers, including conversion, shift, comparison, addition, subtraction, multiplication, division, and power. The paper analyzes the time complexity of each of the algorithms in the amount of bit operations, presents the source code of the power operation in C, and gives some examples which are utilized for validating the correctness of the algorithms according to the properties of a group.