2022 Fiscal Year Research-status Report
New Paradigm to Construct Public Key Cryptographic Schemes for Lightweight Devices with Provable Security against Quantum Attackers
| Project/Area Number |
18K11292
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| Research Institution | The University of Electro-Communications |
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Principal Investigator |
SANTOSO BAGUS 電気通信大学, 大学院情報理工学研究科, 准教授 (40571956)
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| Co-Investigator(Kenkyū-buntansha) |
太田 和夫 電気通信大学, 大学院情報理工学研究科, 特任教授 (80333491)
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| Project Period (FY) |
2018-04-01 – 2024-03-31
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| Keywords | post-quantum / identification scheme / MQ polynomials / MinRank problem / encryption scheme / NP-hard |
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| Outline of Annual Research Achievements |
In FY 2022, we successfully completed our proposed construction of the post-quantum interactive public-key identification (ID) scheme whose security is based on the hardness of MinRank problem. Since MinRank problem is a computational problem based on binary field, our ID scheme is directly representable in binary field. This makes our scheme to be easily implementable in today's real-world hardwares as most of them are constructed based on electronic circuits which execute binary field operation.
We also successfully invented a new computational problem based on multivariate quadratic (MQ) polynomials which is proven to be NP-hard. Based on the new computational problem, we constructed a new post-quantum public-key ID scheme which is proven to be secure as long as the new computational problem is hard. Moreover, since the computational problem can be represented directly in binary field, the new ID scheme is also fully representable directly in binary field.
In the other line of research, we successfully derived the capacity region for secure symmetric-key encryption under real-time side-channel attacks where the adversary obtains side-channel information on the secret key used during the encryption process.
Finally, as a preparation for constructing post-quantum multi-signatures for blockchains, we also proposed a new framework to construct a tightly secure two-round multi-signature scheme. Based on the framework, we built a multi-signature scheme which is easy to implement securely using the standard elliptic curves.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
We have presented our proposed post-quantum public-key ID scheme based on MinRank problem in a peer-reviewed international conference, International Symposium on Information Theory and Its Applications, ISITA 2022.
Meanwhile, we also have published our work on the strong converse for secure symmetric-key encryption scheme against side-channel attacks in the largest peer-reviewed international conference in the field of information theory, i.e., IEEE International Symposium on Information Theory (ISIT) 2022.
We have also presented our newly invented NP-hard computational problem based on multivariate quadratic polynomials along with the constructed ID scheme based on it at the largest domestic security symposium, i.e., Symposium on Cryptography and Information Security (SCIS) 2022. We also presented our work on the tightly secure two-round multi-signature schemes at SCIS 2022.
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| Strategy for Future Research Activity |
We plan to improve the efficiency of our post-quantum ID scheme based on MinRank problem by using the technique of MPC-on-the-head and then transform the ID scheme into a post-quantum digital signature scheme using Fiat-Shamir transform. We also plan to investigate techniques to reduce the communication cost of the newly constructed identification scheme based on the newly invented computational problem based on the multivariate quadratic polynomials. We also plan to measure the hardness of the newly invented computational problem in the average case, since only the worst case hardness has been guaranteed so far. Furthermore, we plan to derive a post-quantum two-round multi-signature scheme based on our proposed framework of multi-signature schemes. We are also interested on Learning Parity with Noises (LPN) problem and the related public-key cryptographic primitives, e.g., public-key encryption schemes, identification schemes. We plan to investigating the hardness of LPN problem and techniques to improve the efficiency or security of the existing LPN based cryptographic primitives, and then propose the new LPN based schemes.
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| Causes of Carryover |
Due to the Covid-19 pandemic, most of conferences can be participated on by online. Thus, there is some leftover from the budget which was planned to use for the travel expenses. We will plan to buy the supporting equipment for computers which will be required for the simulation and/or the experiment at the final stage of our research project in FY 2023.
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