© Marius Iulian Mihailescu and Stefania Loredana Nita 2021
M. I. Mihailescu, S. L. NitaPro Cryptography and Cryptanalysis https://doi.org/10.1007/978-1-4842-6367-9_3

3. Large Integer Arithmetic

Marius Iulian Mihailescu1   and Stefania Loredana Nita1
Bucharest, Romania

During the complex implementation of complex cryptographic algorithms, operations based on large integers are difficult tasks to be achieved. Most of the limitations are due to hardware equipment (e.g. processor, RAM memory) or programming languages.

In C#, an integer value is represented as 32 bits. From those 32 bits, only 31 are used to represent positive integer arithmetic. In cryptography, it’s recommended that we deal with numbers up to two billion, 2 · 109.

Most compilers, such ...

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