Equivalent Keys: Side-Channel Countermeasure for Post-Quantum Multivariate Quadratic Signatures
Algorithms based on the hardness of solving multivariate quadratic equations present promising candidates for post-quantum digital signatures. Contemporary threats to implementations of cryptographic algorithms, especially in embedded systems, include side-channel analysis, where attacks such as dif...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-11-01
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| Series: | Electronics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2079-9292/11/21/3607 |
| _version_ | 1797468542539399168 |
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| author | David Pokorný Petr Socha Martin Novotný |
| author_facet | David Pokorný Petr Socha Martin Novotný |
| author_sort | David Pokorný |
| collection | DOAJ |
| description | Algorithms based on the hardness of solving multivariate quadratic equations present promising candidates for post-quantum digital signatures. Contemporary threats to implementations of cryptographic algorithms, especially in embedded systems, include side-channel analysis, where attacks such as differential power analysis allow for the extraction of secret keys from the device’s power consumption or its electromagnetic emission. To prevent these attacks, various countermeasures must be implemented. In this paper, we propose a novel side-channel countermeasure for multivariate quadratic digital signatures through the concept of equivalent private keys. We propose a random equivalent key to be generated prior to every signing, thus randomizing the computation and mitigating side-channel attacks. We demonstrate our approach on the Rainbow digital signature, but since an unbalanced oil and vinegar is its special case, our work is applicable to other multivariate quadratic signature schemes as well. We analyze the proposed countermeasure regarding its properties such as the number of different equivalent keys or the amount of required fresh randomness, and we propose an efficient way to implement the countermeasure. We evaluate its performance regarding side-channel leakage and time/memory requirements. Using test vector leakage assessment, we were not able to detect any statistically significant leakage from our protected implementation. |
| first_indexed | 2024-03-09T19:07:55Z |
| format | Article |
| id | doaj.art-ed7cc0fd7f4c4d50967abc798e073f7d |
| institution | Directory Open Access Journal |
| issn | 2079-9292 |
| language | English |
| last_indexed | 2024-03-09T19:07:55Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Electronics |
| spelling | doaj.art-ed7cc0fd7f4c4d50967abc798e073f7d2023-11-24T04:26:39ZengMDPI AGElectronics2079-92922022-11-011121360710.3390/electronics11213607Equivalent Keys: Side-Channel Countermeasure for Post-Quantum Multivariate Quadratic SignaturesDavid Pokorný0Petr Socha1Martin Novotný2Department of Digital Design, Faculty of Information Technology, Czech Technical University in Prague, 160 00 Prague, Czech RepublicDepartment of Digital Design, Faculty of Information Technology, Czech Technical University in Prague, 160 00 Prague, Czech RepublicDepartment of Digital Design, Faculty of Information Technology, Czech Technical University in Prague, 160 00 Prague, Czech RepublicAlgorithms based on the hardness of solving multivariate quadratic equations present promising candidates for post-quantum digital signatures. Contemporary threats to implementations of cryptographic algorithms, especially in embedded systems, include side-channel analysis, where attacks such as differential power analysis allow for the extraction of secret keys from the device’s power consumption or its electromagnetic emission. To prevent these attacks, various countermeasures must be implemented. In this paper, we propose a novel side-channel countermeasure for multivariate quadratic digital signatures through the concept of equivalent private keys. We propose a random equivalent key to be generated prior to every signing, thus randomizing the computation and mitigating side-channel attacks. We demonstrate our approach on the Rainbow digital signature, but since an unbalanced oil and vinegar is its special case, our work is applicable to other multivariate quadratic signature schemes as well. We analyze the proposed countermeasure regarding its properties such as the number of different equivalent keys or the amount of required fresh randomness, and we propose an efficient way to implement the countermeasure. We evaluate its performance regarding side-channel leakage and time/memory requirements. Using test vector leakage assessment, we were not able to detect any statistically significant leakage from our protected implementation.https://www.mdpi.com/2079-9292/11/21/3607embedded systemsmultivariate quadratic signaturepost-quantum cryptographyside-channel security |
| spellingShingle | David Pokorný Petr Socha Martin Novotný Equivalent Keys: Side-Channel Countermeasure for Post-Quantum Multivariate Quadratic Signatures Electronics embedded systems multivariate quadratic signature post-quantum cryptography side-channel security |
| title | Equivalent Keys: Side-Channel Countermeasure for Post-Quantum Multivariate Quadratic Signatures |
| title_full | Equivalent Keys: Side-Channel Countermeasure for Post-Quantum Multivariate Quadratic Signatures |
| title_fullStr | Equivalent Keys: Side-Channel Countermeasure for Post-Quantum Multivariate Quadratic Signatures |
| title_full_unstemmed | Equivalent Keys: Side-Channel Countermeasure for Post-Quantum Multivariate Quadratic Signatures |
| title_short | Equivalent Keys: Side-Channel Countermeasure for Post-Quantum Multivariate Quadratic Signatures |
| title_sort | equivalent keys side channel countermeasure for post quantum multivariate quadratic signatures |
| topic | embedded systems multivariate quadratic signature post-quantum cryptography side-channel security |
| url | https://www.mdpi.com/2079-9292/11/21/3607 |
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