Table of Links Abstract and 1. Introduction Abstract and 1. Introduction Contribution


Related Work


Brief of Homomorphic Polynomial Public Key Cryptography and 4.1 DPPK
4.2 MPPK Key Encapsulation Mechanism
4.3 HPPK KEM
4.4 MPPK DS


HPPK Digital Signature Scheme
5.1 HPPK DS Algorithm
5.2 Signing
5.3 Verify
5.4 A Variant of the Barrett Reduction Algorithm
5.5 A Toy Example


HPPK DS Security Analysis


Conclusion, References, Acknowledgements, and Author contributions statement Contribution Contribution Contribution Related Work Related Work Related Work Brief of Homomorphic Polynomial Public Key Cryptography and 4.1 DPPK
4.2 MPPK Key Encapsulation Mechanism
4.3 HPPK KEM
4.4 MPPK DS Brief of Homomorphic Polynomial Public Key Cryptography and 4.1 DPPK Brief of Homomorphic Polynomial Public Key Cryptography and 4.1 DPPK 4.2 MPPK Key Encapsulation Mechanism 4.2 MPPK Key Encapsulation Mechanism 4.3 HPPK KEM 4.3 HPPK KEM 4.4 MPPK DS 4.4 MPPK DS HPPK Digital Signature Scheme
5.1 HPPK DS Algorithm
5.2 Signing
5.3 Verify
5.4 A Variant of the Barrett Reduction Algorithm
5.5 A Toy Example HPPK Digital Signature Scheme HPPK Digital Signature Scheme 5.1 HPPK DS Algorithm 5.1 HPPK DS Algorithm 5.2 Signing 5.2 Signing 5.3 Verify 5.3 Verify 5.4 A Variant of the Barrett Reduction Algorithm 5.4 A Variant of the Barrett Reduction Algorithm 5.5 A Toy Example 5.5 A Toy Example HPPK DS Security Analysis HPPK DS Security Analysis HPPK DS Security Analysis Conclusion, References, Acknowledgements, and Author contributions statement Conclusion, References, Acknowledgements, and Author contributions statement Conclusion, References, Acknowledgements, and Author contributions statement 4 Brief of Homomorphic Polynomial Public Key Cryptography In this section, we are going to briefly describe the motivation behind and development of the HPPK scheme: the path from the original deterministic polynomial public key or DPPK, proposed by Kuang in 2021[1], then multivariate polynomial public key or MPPK, proposed by Kuang, Perepechaenko, and Barbeau in 2022[5], to the homomorphic polynomial public key over a single hidden ring in 2023[6], and over a dual hidden ring scheme[7]. MPPK schemes for digital signature or MPPK/DS have been proposed by Kuang, Perepechaenko, and Barbeau in 2022[8], then an optimized version was proposed by Kuang and Perepechaenko in 2023[9]. A forged signature attack was reported by Guo in 2023[10]. 4.1 DPPK 4.2 MPPK Key Encapsulation Mechanism 4.3 HPPK KEM 4.4 MPPK DS A digital signature scheme based on MPPK has been proposed by Kuang, Perepechaenko, and Barbeau in 2022[8] and later optimized variant was proposed by Kuang and Perepechaenko in 2023[9]. MPPK digital signature scheme originated from MPPK over a single prime field[3, 4]. The signature verification equation stems from the identity equation Authors:
(1) Randy Kuang, Quantropi Inc., Ottawa, K1Z 8P9, Canada (randy.kuang@quantropi.com);
(2) Maria Perepechaenko, Quantropi Inc., Ottawa, K1Z 8P9, Canada;
(3) Mahmoud Sayed, Systems and Computer Engineering, Carleton University, Ottawa, K1S 5B6, Canada;
(4) Dafu Lou, Quantropi Inc., Ottawa, K1Z 8P9, Canada. Authors: Authors: (1) Randy Kuang, Quantropi Inc., Ottawa, K1Z 8P9, Canada (randy.kuang@quantropi.com); (2) Maria Perepechaenko, Quantropi Inc., Ottawa, K1Z 8P9, Canada; (3) Mahmoud Sayed, Systems and Computer Engineering, Carleton University, Ottawa, K1S 5B6, Canada; (4) Dafu Lou, Quantropi Inc., Ottawa, K1Z 8P9, Canada. This paper is available on arxiv under ATTRIBUTION-NONCOMMERCIAL-SHAREALIKE 4.0 INTERNATIONAL license. This paper is available on arxiv under ATTRIBUTION-NONCOMMERCIAL-SHAREALIKE 4.0 INTERNATIONAL license. available on arxiv available on arxiv

Part of HackerNoon's growing list of open-source research papers, promoting free access to academic material.

The Barrett Algorithm Reimagined for Post-Quantum Signatures

Why Ethics Fail in Open Source Communities

EScholar Technologies

Too Long; Didn't Read

CTA: Download the FREE AI Productivity Shift report

What You Should Know About the Next Generation of Encryption

About Author

Comments

TOPICS

THIS ARTICLE WAS FEATURED IN

Related Stories

Untitled Story

How HPPK DS Balances Security and Efficiency Across NIST Levels

The Barrett Algorithm Reimagined for Post-Quantum Signatures

A Beginner’s Guide to the HPPK Digital Signature Scheme

How HPPK DS Balances Security and Efficiency Across NIST Levels

Exploring Decentralization With Homomorphic Encryption

How HPPK DS Balances Security and Efficiency Across NIST Levels

The Barrett Algorithm Reimagined for Post-Quantum Signatures

A Beginner’s Guide to the HPPK Digital Signature Scheme

How HPPK DS Balances Security and Efficiency Across NIST Levels

Exploring Decentralization With Homomorphic Encryption

Light-Mode

Classic

Newspaper

Dark-Mode

Neon Noir

Minty

HN StartUps