The goal is to help students gain skills and fundamental knowledge on finite fields, cryptography, and error correcting codes.

Upon successful completion of this module, students will be able to:
1. Describe the fundamental mathematical concepts of and perform computations in finite fields - Finite fields
2. Analyse, deploy, and design encryption/decryption and digital signature schemes for secure information exchange – Cryptography
3. Detect and correct communication errors using popular error correcting codes, including Hamming codes, Reed-Solomon codes, and/or BCH codes, for reliable information exchange – Error correcting codes

Finite fields: definition, properties, primitive element, and polynomial factorisation on finite fields;
Cryptography: password storage and sharing, secret sharing, public key systems, and digital signature;
Concepts of error detection and correction. Linear codes, generator and parity checking matrices, distance, and Hamming codes;
Bounds to the performance of codes;
Reed Solomon codes, Cyclic and BCH codes;