What You Should Know About the Next Generation of Encryption

Table of Links

Abstract and 1. Introduction

1. Contribution

2. Related Work

3. 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

4. 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

5. HPPK DS Security Analysis

6. 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

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4.2 MPPK Key Encapsulation Mechanism

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4.3 HPPK KEM

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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

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:::info 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.

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:::info This paper is available on arxiv under ATTRIBUTION-NONCOMMERCIAL-SHAREALIKE 4.0 INTERNATIONAL license.

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