A deep dive into computing multiplicative inverses in both modular integer arithmetic and finite fields GF(2)[x], using Blankinship's constant-space variant of the Extended Euclidean Algorithm. The post walks through the algorithm step by step with numeric tables, polynomial long division examples, and Python code snippets. It also explains the practical relevance: multiplicative inverses underpin RSA encryption and discrete logarithm tricks used in cryptographic systems and LFSR-based applications.
