| 研究課題/領域番号 |
18K11292
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| 研究機関 | 電気通信大学 |
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研究代表者 |
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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| 研究分担者 |
太田 和夫 電気通信大学, 大学院情報理工学研究科, 特命教授 (80333491)
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| 研究期間 (年度) |
2018-04-01 – 2022-03-31
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| キーワード | encryption / multivariate polynomials |
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| 研究実績の概要 |
In FY 2020, we have successfully constructed a new El-Gamal like encryption scheme based on Multivariate Quadratic Polynomials (MQ). The most important features of the constructed scheme are not only that it can be represented directly in the binary field (GF(2)), but it also indicates a possible extension to Diffie-Hellman (DH)-like key exchange. It should be noted that there has no secure drop-in replacement for DH key exchange based on MQ yet. Our encryption scheme is provable secure based on the hardness assumption of newly formulated computational problems based on MQ. One can see the computational problems as analogous to the Discrete Logarithm Problem (DLP), Computational DH (CDH) and the Decisional DH (DDH) in the general group. Since problems based on MQ may promise hardness even against quantum computers, there exists a high possibility that the new encryption scheme may offer provable security against quantum computers. Assuming that these new problems are hard for quantum computers, a large number of protocols based on DLP, CDH, or DDH in the general group can be directly transformed into post-quantum secure protocols. Therefore, we also constructed a new aggregate signature scheme that can be implemented in any algebraic group. Our scheme offers an offline/online feature which is very useful for implementation in lightweight devices which low resources. In the heart of our security proof of the proposed scheme is the new technique to avoid the open signing query attack which had rendered lots of multi signatures and aggregate signatures insecure.
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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
2: おおむね順調に進展している
理由
In FY 2020, we have successfully constructed a new El-Gamal like encryption scheme based on Multivariate Quadratic Polynomials (MQ). And this research result has been published in the most prominent international peer-reviewed conference for post-quantum cryptography, i.e., PQCrypto 2020. We also have successfully constructed a new secure aggregate signature scheme that can be implemented in any algebraic group. The research result has been published in a peer-reviewed international conference focusing on provable security, i.e., Provsec 2020. Another research result is the reevaluation of the complexity of the Learning With Errors (LWE) problem which is the foundation of the security of lattice-based cryptographic schemes which are the strongest candidate for the standard post-quantum cryptography. This research result has been published as a technical report and has been presented in a regular technical meeting group focusing on information theory and its applications. The presentation was awarded as the best student presentation.
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| 今後の研究の推進方策 |
In FY 2021, we plan to perform various tests on the security of the encryption scheme which we constructed in FY2020 and published in PQCrypto 2020. We plan to perform theoretical tests by lifting the algebraic structure used in the encryption scheme into an extended field and investigate the complexity of solving the MQ based problems which are the security foundation of the encryption scheme. We also plan to perform a practical security test by transforming the MQ based problems into pure MQ problems. We then find the solving degree of regularity when put the MQ problems into Groebner basis algorithm such as F4 algorithm in Magma. We also try to develop new signature schemes based on the MQ problems and prove their security against quantum adversary in single user and multi user settings.
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| 次年度使用額が生じた理由 |
コロナの影響で世界中の国の政府からの移動制限があり、研究会や学会等はほとんどオンラインで行われ、予定した旅費が使えなくなった。大学もほとんどオンラインになり、
予定した作業の計画に変更が生じ、2020年度の人件費・謝金を使用せず、2021年度に使いまわすという予定立てています。
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