Software Implementation of Cryptographic Sequence Generators over Extended Fields

Linear Feedback Shift Registers (LFSRs) are currently used as generators of pseudorandom sequences with multiple applications from communication systems to cryptography. In this work, design and software implementation of LFSRs defined over extended fields GF(2ⁿ) instead of over the binary field GF(2) are analysed. The key idea is combining algebraic structures (finite fields) with modern processor capabilities to take advantage of the underlying device over which the application is executed. The study has been carried out for diverse extended fields and different architectures. Detailed microanalysis and macroanalysis of the LFSR implementation are performed too. Numerical results prove that extended fields provide speedup factors up to 10.15. The benefits of these fields are clear for applications with LFSRs cryptographic applications, including