The goal is to help you gain skills and fundamental knowledge on finite fields, cryptography, and error-correcting codes. You will learn about computations in finite fields, secure information exchange using encryption/decryption and digital signature schemes, and correcting communication errors using popular error-correcting codes for reliable information exchange.

Upon successful completion of this module, you will be able to: 1 Compute parameters in finite fields using the fundamental mathematical concepts - Finite fields 2 Design and analyse encryption/decryption schemes for secure information exchange – Cryptography 3 Create digital signature schemes for secure information exchange – Cryptography 4 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;