Residue Number System Ring Generator for Cryptographic Sequence Extension

The patent segments the finite field expansion problem by using multiple relatively prime moduli (m1, m2, ..., mk) instead of a single large modulus. Each modulus generates a smaller field GF[mi], and the Chinese Remainder Theorem combines these fields to achieve the desired expanded field size. This segmentation allows efficient computation in smaller fields while achieving the security requirements of larger fields.

The patent introduces the Chinese Remainder Theorem as an intermediary mechanism that efficiently combines results from multiple smaller finite fields into a larger field. This intermediary allows the system to leverage the computational efficiency of small field operations while achieving the expanded field size needed for cryptographic security.

The patent changes the fundamental parameters of the scrambling approach by moving from fixed S-box functions to dynamic permutation orderings generated by ring generators. The ring generator uses irreducible polynomials and finite field arithmetic to create variable permutations that adapt to different input sequences, achieving high entropy without the fixed computational overhead of conventional S-box methods.

The patent introduces dynamic permutation orderings that change based on the input data and cryptographic key, rather than using static S-box tables. The ring generator dynamically computes permutations using finite field arithmetic, allowing the scrambling to adapt to different patterns and achieve higher entropy while maintaining computational efficiency through structured algebraic operations.