Homomorphic polynomial public key with the Barrett transformation for digital signature
Bibliographic record
Abstract
In their 2022 study, Kuang et al. introduced the multivariable polynomial public key (MPPK) cryptography, which is a quantum-safe public key cryptosystem that leverages the inversion relationship between multiplication and division. MPPK uses multiplication for key pair construction and division for decryption, generating public multivariate polynomials. Kuang and Perepechaenko expanded this into the homomorphic polynomial public key (HPPK) by transforming product polynomials over large hidden rings using homomorphic encryption. Initially designed for key encapsulation mechanism (KEM), HPPK ensures the security of public polynomials over concealed rings through homomorphic encryption. This article extends HPPK for KEM (HPPK KEM) to a digital signature (DS) scheme. To adapt HPPK KEM for DSs, we introduce an extension of the Barrett reduction algorithm which transforms modular multiplications over hidden rings into divisions in the verification equation. This extension nonlinearly embeds the signature into public polynomial coefficients, employing the floor function of large integer divisions. Our proposed scheme addresses forgery attacks observed in previous MPPK DS schemes by leveraging dual hidden rings and the Barrett reduction algorithm. This method provides nonlinear encryption for the HPPK public key, preventing shortcuts other than brute-force searches. Integrating signature elements into public polynomial coefficients adds complexity to forged signature attacks, with the nonlinear Barrett transformation significantly enhancing security. A toy example illustrates the functionality of the HPPK DS scheme, and security analysis indicates it achieves exponential complexity for both private key recovery and forged signature attacks. Future research will benchmark performance and compare it with National Institute of Standards and Technology (NIST)-standardized algorithms.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.006 | 0.005 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".