Group Re-keying Protocol Based on Modular Polynomial Arithmetic Over Galois Field GF(2ⁿ)

Abstract

Problem statement: In this study we propose a group re-keying protocol based on modular polynomial arithmetic over Galois Field GF(2ⁿ). Common secure group communications requires encryption/decryption for group re-keying process, especially when a group member is leaving the group. Approach: This study proposes secret keys multiplication protocol based on modular polynomial arithmetic (SKMP), which eliminates the need for the encryption/decryption during the group re-keying. Results: The implementation based on modular polynomial arithmetic over Galois Field GF(2ⁿ) offers fast re-keying process (about 50% faster than Secret Keys Multiplication Protocol (SKM) for 128 bit key) and compact key size representation against other secret keys multiplication protocols. With SKMP group re-keying is handled more efficiently through modular polynomial arithmetic manipulation rather than the expensive encryption/encryption which need to be done on every membership change.