APPLICATION OF ADDITIVE GROUP COSETS OF INTEGER SETS IN CRYPTOGRAPHIC ALGORITHMS

Abstract

Cryptography is a field of science that studies information and communication security by converting messages into an unreadable, unalterable form and confirming the identities of the sender and recipient. Cosets of a group are sets formed by the action of a subgroup on elements of the group, yielding equivalence classes that partition the group into several mutually disjoint subsets. This research discusses the application of additive group cosets, namely the set of all integers Z, to the design of cryptographic algorithms. In this research, the subgroup used to form the cosets is the 60ℤ subgroup. Furthermore, the set of ℤ/60ℤ cosets will be used in the design of cryptographic algorithms for encryption and decryption. The cryptographic algorithm design is implemented as an encryption-decryption program in C++, using the group cosets approach. The research results are a cryptographic algorithm design based on the coset set ℤ/60ℤ, implemented in C++. The use of cosets on ℤ/60ℤ can strengthen the security of the cryptographic algorithm by dividing messages into equivalence classes, making it more difficult to recover messages without the correct key.