Finite Field Arithmetic studies mathematical properties of finite rings and fields in order to discover novel representations of the elements and fast algorithms for arithmetic operations for designing efficient software and hardware for cryptography and error-correcting codes.

Random Number Generators are used for supplying secret keys, private keys, and ephemeral and initializing variables in cryptographic systems. Its foundations are based on cryptographic randomness, in terms of its entropy under the different measures and its complexity as methods of representation and underlying mathematical functions.

Homomorphic Encryption is a form of encryption that allows computations to be performed on encrypted data without decrypting it. Homomorphic encryption is used for privacy-preserving outsourced storage and computation. This allows data to be encrypted and out-sourced to commercial cloud environments for processing, while remain encrypted.

Machine Learning is a field of study in artificial intelligence concerned with the development and study of algorithms that can learn from data and generalize, and thus perform tasks without explicit instructions. Machine learning approaches have been applied to many fields including large language models, computer vision, speech recognition, agriculture, and medicine.