Work

Modular Mirror: Efficient Residue Prediction in Primitive Root Cycles

Year: 2026

Type: article

Abstract: This paper presents a simplified method for calculating modular residues in thesecond half of a primitive root’s power cycle. We demonstrate that for any oddprime p and primitive root a, the residues of the second half of the cycle (k > p−12 )are simply the additive inverses (reflections) of the first half. This ”Modular Mirror”rule allows for the determination of residues via a single subtraction (p−r), provingcomputationally superior to standard modular inverse methods when the order ofthe element is p − 1.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.19582711

Author: Noguera R., Luis C.

Language: English

Topic: Cryptography and Residue Arithmetic

Subfield: Information Systems

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7154248290

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