Table of Links
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Brief of Homomorphic Polynomial Public Key Cryptography and 4.1 DPPK
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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 ([email protected]);
(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