Papers

Preprints

In preparation

1. Momonari Kudo, Tomoki Moriya, and Ryo Ohashi, "Computational enumeration of superspecial Howe curves of genus five", in preparation.

Under submission

2. Momonari Kudo and Kazuhiro Yokoyama, "The solving degrees of affine semi-regular polynomial sequences", arXiv:2404.03530 [math.AC] (or IACR Cryptology ePrint Archive, 2024/528), 26 pages, 2024, submitted.

3. Ryo Ohashi, Hiroshi Onuki, Momonari Kudo, Ryo Yoshizumi, and Koji Nuida, "Computing Richelot isogeny graph of superspecial abelian threefolds", arXiv: 2401.10500 [math.AG], 22 pages, 2024, submitted.

4. Momonari Kudo, "Explicit construction of a plane sextic model for genus-five Howe curves, II", arXiv: 2401.00760 [math.AG], 19 pages, 2024, submitted.

5. Ryo Ohashi and Momonari Kudo, "Computing superspecial hyperelliptic curves of genus 4 with automorphism group properly containing the Klein 4-group", arXiv: 2312.16858 [math.AG], 26 pages, 2023, submitted.

6. Tomoki Moriya and Momonari Kudo, "Explicit construction of a plane sextic model for genus-five Howe curves, I", arXiv: 2310.15993 [math.AG], 24 pages, 2023, submitted.

7. Kosuke Sakata, Taku Kato, Momonari Kudo and Kazuhiro Yokoyama, "On Computing Groebner bases over exterior algebra", 19 pages, 2022, submitted.

8. Tomoki Moriya and Momonari Kudo, "Some explicit arithmetics on curves of genus three and their applications", arXiv: 2209.02926 [math.AG], 34 pages, 2022, submitted.

9. Momonari Kudo and Shushi Harashita, "Computing the space of differential forms of a plane curve and its Cartier-Manin matrix", arXiv: 2203.11801 [math.AG], 27 pages, 2022, submitted.

10. Momonari Kudo, "Attacks against search Poly-LWE", IACR Cryptology ePrint Archive, 2016/1153, 29 pages, 2016, submitted.

Refereed Papers

International Journal

• 1. Ryo Ohashi, Momonari Kudo and Shushi Harashita, "The a-numbers of non-hyperelliptic curves of genus three with large cyclic automorphism group", Acta Arithmetica, 23 pages, to appear (preprint ver: arXiv: 2111.09777 [math.AG]).

  2. Momonari Kudo and Kazuhiro Yokoyama, "On Hilbert-Poincare series of affine semi-regular polynomial sequences and related Groebner bases", In: T. Takagi et al. (eds), Mathematical Foundations for Post-Quantum Cryptography, Mathematics for Industry, 26 pages, Springer, to appear (preprint ver: arXiv: 2401.07768 [cs.SC]).

  3. Momonari Kudo and Shushi Harashita, "Computational search for superelliptic curves attaining the gonality-point bound, with extra genus-5 examples", Commentarii Mathematici Universitatis Sancti Pauli, 24 pages, to appear (preprint ver: arXiv: 2204.06805 [math.AG]).

  4. Momonari Kudo and Shushi Harashita, "Representation of non-special curves of genus 5 as plane sextic curves and its application to finding curves with many rational points", Journal of Symbolic Computation, Vol. 122, 15 pages, 2023, (DOI) https://doi.org/10.1016/j.jsc.2023.102272  (preprint ver: arXiv: 2102.07270 [math.AG])

  5. Momonari Kudo, Tasuku Nakagawa and Tsuyoshi Takagi, "Efficient search for superspecial hyperelliptic curves of genus four with automorphism group containing C6", to appear in Mathematics in Computer Science , Vol. 17, 21 pages, 2023, (DOI)  https://doi.org/10.1007/s11786-023-00571-w (preprint ver: arXiv: 2210.14822 [math.AG]).

  6. Momonari Kudo and Shushi Harashita, "Algorithmic study of superspecial hyperelliptic curves over finite fields", Commentarii Mathematici Universitatis Sancti Pauli, Vol. 70,  49-64, 2022, (DOI) doi/10.14992/00022411.

  7. Momonari Kudo and Shushi Harashita, "Superspecial trigonal curves of genus 5", Experimental Mathematics, Vol. 31, Issue 3, 908-919, 2022, (DOI) 10.1080/10586458.2020.1723745 (preprint ver: arXiv:1804.11277 [math.AG]).

  8. Yuta Kambe, Masaya Yasuda, Masayuki Noro, Kazuhiro Yokoyama, Yusuke Aikawa, Katsuyuki Takashima and Momonari Kudo, "Solving the constructive Deuring correspondence via the Kohel-Lauter-Petit-Tignol algorithm", Mathematical Cryptology, Vol. 1, No. 2, 10-24, 2022, Retrieved from https://journals.flvc.org/mathcryptology/article/view/130618.

  9. Momonari Kudo, "Computing representation matrices for the action of Frobenius on cohomology groups", Journal of Symbolic Computation, Vol. 109, 441-464, 2022, (DOI) 10.1016/j.jsc.2020.07.015.

  10. Yasushi Takahashi, Momonari Kudo, Ryoya Fukasaku, Yasuhiko Ikematsu, Masaya Yasuda and Kazuhiro Yokoyama, "Algebraic approaches for solving isogeny problems of prime power degrees", Journal of Mathematical Cryptology, Vol. 15, Issue 1, 31-44, 2020, (DOI) https://doi.org/10.1515/jmc-2020-0072.

  11. Momonari Kudo, Shushi Harashita and Hayato Senda, "The existence of supersingular curves of genus 4 in arbitrary characteristic", Research in Number Theory, Vol. 6, Issue 4, Article number: 44, 17 pages, 2020, (DOI) https://doi.org/10.1007/s40993-020-00217-x.

  12. Momonari Kudo, Shushi Harashita and Hayato Senda, "Automorphism groups of superspecial curves of genus 4 over F11", Journal of Pure and Applied Algebra, Vol. 224, Issue 9, 19 pages, 2020, (DOI) 10.1016/j.jpaa.2020.106339.

  13. Momonari Kudo and Shushi Harashita, "Computational approach to enumerate non-hyperelliptic superspecial curves of genus 4", Tokyo Journal of Mathematics, Vol. 43, Number 1, 259-278, 2020, (DOI) doi:10.3836/tjm/1502179310.

  14. Momonari Kudo, "On the existence of superspecial and maximal nonhyperelliptic curves of genera four and five", Communications in Algebra, Vol. 47, Issue 12, 5020-5038, 2019, (DOI) 10.1080/00927872.2019.1609013 (this is an article putting results in arXiv:1804.09063 [math.AG] and in arXiv:1807.04394 [math.AG] together).

  15. Jintai Ding, Momonari Kudo, Shinya Okumura, Tsuyoshi Takagi and Chengdong Tao, "Cryptanalysis of a public key cryptosystem based on Diophantine equations via weighted LLL reduction", Japan Journal of Industrial and Applied Mathematics, Vol. 35, Issue 3, 1123-1152, 2018, (DOI) 10.1007/s13160-018-0316-x.

  16. Momonari Kudo and Shushi Harashita, "Superspecial curves of genus 4 in small characteristic", Finite Fields and Their Applications, Vol. 45, 131-169, 2017, (DOI) 10.1016/j.ffa.2016.12.001.

  17. Momonari Kudo, "Analysis of an algorithm to compute the cohomology groups of coherent sheaves and its applications", Japan Journal of Industrial and Applied Mathematics, Vol. 34, Issue 1, 1-40, 2017, (DOI) 10.1007/s13160-017-0238-z.

 RIMS Kokyuroku Bessatsu

1. Momonari Kudo and Shushi Harashita, "Introduction to Computational Algebraic Geometry", RIMS Kokyuroku Bessatsu (Algebraic Number Theory and Related Topics 2020), 23 pages, to appear.

2. Ryoya Fukasaku, Yasuhiko Ikematsu, Momonari Kudo, Masaya Yasuda and Kazuhiro Yokoyama, "Introduction to algebraic approaches for solving isogeny path-finding problems", RIMS Kokyuroku Bessatsu (Theory and Applications of Supersingular Curves and Supersingular Abelian Varieties), B90, 169-184, 2022, http://hdl.handle.net/2433/276280.

3. Momonari Kudo, "Counting isomorphism classes of superspecial curves", RIMS Kokyuroku Bessatsu (Theory and Applications of Supersingular Curves and Supersingular Abelian Varieties), B90, 77-95, 2022, http://hdl.handle.net/2433/276274.

Japanese Articles

1. 工藤桃成, "計算代数幾何学の現在 ―連接層のコホモロジー群と正標数の代数曲線にまつわる算術を中心に―", 日本数学会「数学」, 巻号未定, 受理済. 

2. 工藤桃成, "代数多様体のコホモロジー群へのフロベニウス作用を計算するアルゴリズム", 日本数式処理学会論文誌「数式処理」, 第29巻2号, 3-30, 2023.

Conference Proceedings

1. Momonari Kudo and Kazuhiro Yokoyama, "The solving degrees of affine semi-regular polynomial sequences", accepted for presentation at MEGA2024: Effective Methods in Algebraic Geometry, 26 pages, to appear.

2. Tomoki Moriya and Momonari Kudo, "Some explicit arithmetic on curves of genus three and their applications", accepted for presentation at MEGA2024: Effective Methods in Algebraic Geometry, 34 pages, 2024, to appear.

3. Hiroki Furue and Momonari Kudo, "Polynomial XL: A Variant of the XL Algorithm Using Macaulay Matrices over Polynomial Rings", In ; Proceedings of PQCrypto 2024, to appear.

4. Haiming Zhu, Shoichi Kamada, Momonari Kudo and Tsuyoshi Takagi, "Improved Hybrid Attack via Error-Splitting Method for Finding Quinary Short Lattice Vectors", Advances in Information and Computer Security, IWSEC 2023, Lecture Notes in Computer Science, Vol. 14128, pp. 117-136, Springer, Cham, 2023, (DOI) https://doi.org/10.1007/978-3-031-41326-1_7.

5. Shinya Okumura, Shusaku Uemura and Momonari Kudo, "Revisiting lattice-based attacks using trace map for Ring-LWE",  In: Proceedings of 2022 International Symposium on Information Theory and Its Applications (ISITA 2022), 5 pages, to appear.

6. Ryo Ohashi, Momonari Kudo and Shushi Harashita, "Fast enumeration of superspecial hyperelliptic curves of genus 4 with automorphism group V4", In: S. Mesnager, Z. Zhou (eds), Arithmetic of Finite Fields, WAIFI 2022, Lecture Notes in Computer Science, Vol. 13638, pp. 107-124, Springer, Cham, 2023, (DOI)  https://doi.org/10.1007/978-3-031-22944-2_6 .

7. Hiroki Furue and Momonari Kudo, "On the computational enumeration of superspecial curves: A survey and complements" (extended abstract), Computer Algebra in Scientific Computing (CASC 2022), 4 pages, 2022.

8. Kosuke Sakata, Momonari Kudo, Taku Kato and Kazuhiro Yokoyama, "Implementation report on computing Groebner bases over exterior algebras" (extended abstract), Computer Algebra in Scientific Computing (CASC 2022), 4 pages, 2022.

9. Tasuku Nakagawa, Mononari Kudo and Tsuyoshi Takagi, "Efficient search for superspecial hyperelliptic curves in large characteristic" (extended abstract), Computer Algebra in Scientific Computing (CASC 2022), 4 pages, 2022.

10. Yuta Kambe, Yusuke Aikawa, Momonari Kudo, Masaya Yasuda, Katsuyuki Takashima, and Kazuhiro Yokoyama, "Implementation report of the Kohel-Lauter-Petit-Tignol algorithm for the constructive Deuring correspondence", In: Giri, D., Raymond Choo, KK., Ponnusamy, S., Meng, W., Akleylek, S., Prasad Maity, S. (eds), Proceedings of the Seventh International Conference on Mathematics and Computing (ICMC 2021), Advances in Intelligent Systems and Computing, 1412, pp. 953–966, Springer, Singapore, 2022.

11. Shusaku Uemura, Kazuhide Fukushima, Shinsaku Kiyomoto, Momonari Kudo and Tsuyoshi Takagi, "Shortest Vectors in Lattices of Bai-Galbraith's Embedding Attack on the LWR Problem", In: T. Nakanishi, R. Nojima (eds), Advances in Information and Computer Security, IWSEC 2021, Lecture Notes in Computer Science, 12835, pp. 23–41, Springer, 2021.

12. Momonari Kudo and Shushi Harashita, "Parametrizing generic curves of genus five and its application to finding curves with many rational points", accepted for presentation at MEGA 2021: Effective Methods in Algebraic Geometry, 16 pages, 2021.

13. Momonari Kudo, Shushi Harashita and Everett Howe, "Algorithms to enumerate superspecial Howe curves of genus four", pp. 301-316 in Proceedings of the Fourteenth Algorithmic Number Theory Symposium (ANTS-XIV), edited by Steven Galbraith, Open Book Series 4, Mathematical Sciences Publishers, Berkeley, 2020, (DOI) 10.2140/obs.2020.4.301.

14. Yasuhiko Ikematsu, Ryoya Fukasaku, Momonari Kudo, Masaya Yasuda, Katsuyuki Takashima and Kazuhiro Yokoyama, "Hybrid meet-in-the-middle attacks for the isogeny path-finding problem", In: Proceedings of The 7th ACM ASIA Public-Key Cryptography Workshop (APKC 2020), pp. 36-44, ACM press, 2020, (DOI) https://doi.org/10.1145/3384940.3388956.

15. Momonari Kudo, "Computing representation matrices for the Frobenius on cohomology groups", accepted for presentation at MEGA 2019: Effective Methods in Algebraic Geometry, 32 pages, 2019.

16. Momonari Kudo and Shushi Harashita, "Superspecial Hyperelliptic Curves of Genus 4 over Small Finite Fields", In: L. Budaghyan, F. Rodriguez-Henriquez (eds), Arithmetic of Finite Fields, WAIFI 2018, Lecture Notes in Computer Science, Vol. 11321, pp. 58-73, Springer, Cham, 2018, (DOI) 10.1007/978-3-030-05153-2_3. 

17. Momonari Kudo, Yuki Yokota, Yasushi Takahashi and Masaya Yasuda, "Acceleration of Index Calculus for Solving ECDLP over Prime Fields and Its Limitation", In: J. Camenisch, P. Papadimitratos (eds), Cryptology and Network Security, CANS 2018, Lecture Notes in Computer Science, Vol. 11124, pp. 377-393, Springer, Cham, 2018, (DOI) 10.1007/978-3-030-00434-7_19.

18. Momonari Kudo and Shushi Harashita, "Enumerating Superspecial Curves of Genus 4 over Prime Fields", In: Proceedings of The Tenth International Workshop on Coding and Cryptography 2017, WCC 2017, 10 pages (pdf).

19. Yuki Yokota, Momonari Kudo and Masaya Yasuda, "Practical Limit of Index Calculus Algorithms for ECDLP over Prime Fields", In: Proceedings of The Tenth International Workshop on Coding and Cryptography 2017, WCC 2017, 12 pages (pdf).

20. Jintai Ding, Momonari Kudo, Shinya Okumura, Tsuyoshi Takagi, and Chengdong Tao, "Cryptanalysis of a Public Key Cryptosystem Based on Diophantine Equations via Weighted LLL Reduction" (Short Paper), In: K. Ogawa, K. Yoshioka (eds), Advances in Information and Computer Security, IWSEC 2016, Lecture Notes in Computer Science, Vol. 9836, pp. 305-315, Springer, Cham, 2016, (DOI) 10.1007/978-3-319-44524-3_18.

21. Momonari Kudo, Junpei Yamaguchi, Yang Guo, and Masaya Yasuda, "Practical Analysis of Key Recovery Attack against Search-LWE Problem", In: K. Ogawa, K. Yoshioka (eds), Advances in Information and Computer Security, IWSEC 2016, Lecture Notes in Computer Science, Vol. 9836, pp. 164-181, Springer, Cham, 2016, (DOI) 10.1007/978-3-319-44524-3_10.

Thesis

PhD Thesis

• Momonari Kudo, "Study on Computational Algebraic Geometry: Computing the Frobenius on sheaf cohomology and its applications", PhD. thesis, Kyushu University, 93 pages, 2017 (論文ファイル・審査結果等).

Master Thesis

• Momonari Kudo, "On the computation of the dimensions of the cohomology groups of coherent sheaves on a projective space", Master thesis, Kyushu University, 49 pages, 2015 (pdf).

Bachelor Thesis (in Japanese)

• 工藤桃成, "Riemann-Roch の定理とその応用", 広島大学, 33 pages, 2013 (pdf).

Others

Misc

1. 工藤桃成, 横山和弘, "アフィン半正則な多項式列に付随するHilbert 級数と関連するGroebner 基底", RIMS講究録, 巻号未定, 11 pages, to appear.

2. 吉住崚, 小貫啓史, 大橋亮, 工藤桃成, 縫田光司, "B-SIDH に対する Castryck-Decru 攻撃の構成と実装", 2024年暗号と情報セキュリティシンポジウム (SCIS2024), 2024, 8 pages, to appear.

3. 守谷共起, 工藤桃成, "種数3における分解 Richelot 同種写像計算アルゴリズムとその応用", 2023年暗号と情報セキュリティシンポジウム (SCIS2023), 3B4-1, 2023, 8 pages (pdf). 

4. 工藤桃成, 大橋亮, 原下秀士, "Fast enumeration of superspecial hyperelliptic curves of genus 4", 日本応用数理学会2022年年会 「数論アルゴリズムとその応用」(JANT) セッション, 北海道大学, Zoom (On-line), E3-4-3, 2022, 2 pages (pdf). 

5. 守谷共起, 工藤桃成, "種数3における分解 Richelot 同種写像を計算するアルゴリズムとその応用", 日本応用数理学会2022年年会 「数論アルゴリズムとその応用」(JANT) セッション, 北海道大学, Zoom (On-line), E3-4-2, 2022, 2 pages (pdf). 

6. 加藤拓, 坂田康亮, 工藤桃成, 横山和弘, "外積代数における Groebner 基底計算アルゴリズムの計算量評価と実装報告", 日本応用数理学会2022年年会 「数論アルゴリズムとその応用」(JANT) セッション, 北海道大学, Zoom (On-line), E3-3-2, 2022, 2 pages (pdf). 

7. 古江弘樹, 工藤桃成, "A Variant of the XL Algorithm Using the Arithmetic over Polynomial Matrices", RIMS講究録, Vol. 2224, pp. 54-58, 2022.

8. 奥村伸也, 上村周作, 工藤桃成, "トレース写像を用いた Ring-LWE 問題に対する格子攻撃の再考", 2022年暗号と情報セキュリティシンポジウム (SCIS2022), 4A2-3, 2022, 8 pages (pdf).

9. 神戸祐太, 高橋康, 相川勇輔, 工藤桃成, 安田雅哉, 高島克幸, 横山和弘, "SIKEに対する vOW 法の内部関数の新計算手法", 2022年暗号と情報セキュリティシンポジウム (SCIS2022), 2A1-3, 2022, 5 pages (pdf).

10. 古江弘樹, 工藤桃成, "A New Efficient Variant of the XL Algorithm Using the Arithmetic over Polynomial Matrices", 2022年暗号と情報セキュリティシンポジウム (SCIS2022), 1A2-5, 2022, 8 pages (pdf).

11. 工藤桃成, "代数多様体のコホモロジー群へのフロベニウス作用を計算するアルゴリズム", Bulletin of the Japan Society for Symbolic and Algebraic Computations, Vol. 27, No. 1, pp. 27-30, 2021 (pdf).

12. 神戸祐太, 相川勇輔, 工藤桃成, 安田雅哉, 高島克幸, 横山和弘, "Kohel-Lauter-Petit-Tignol アルゴリズムの構成的 Deuring 対応への応用", 2021年暗号と情報セキュリティシンポジウム (SCIS2021), 2A1-1, 2021.

13. 上村周作, 福島和英, 清本晋作, 工藤桃成, 高木剛, "LWR 問題に対する Bai-Galbraith 埋込法の格子に現れる最短ベクトル", 2021年暗号と情報セキュリティシンポジウム (SCIS2021), 2A3-3, 2021, 8 pages (pdf).

14. 大住友輝, 上村周作, 工藤桃成, 高木剛, "格子暗号 SABER に対する鍵不一致攻撃",  2021年暗号と情報セキュリティシンポジウム (SCIS2021), 3A3-2, 2021, 8 pages (pdf).

15. 工藤桃成, 原下秀士, Everett Howe, "Efficient algorithms for finding and enumerating superspecial Howe curves in much larger characteristic", 日本応用数理学会2020年年会 「数論アルゴリズムとその応用」(JANT) セッション, 愛媛大学 Zoom (On-line), 2020, 2 pages (pdf). 

16. 池松泰彦, 深作亮也, 工藤桃成, 安田雅也, 高島克幸, 横山和弘, "同種写像パス探索問題に対する中間一致攻撃のハイブリッド手法", 2020年暗号と情報セキュリティシンポジウム (SCIS2020), 4A2-2, 2020.

17. 高橋康, 工藤桃成, 池松泰彦, 安田雅哉, 横山和弘, "同種写像問題に対する代数的求解法の解析と計算量評価", 日本応用数理学会2019年年会 「数論アルゴリズムとその応用」(JANT) セッション, 東京大学, 2019, 2 pages (pdf).

18. 工藤桃成, 原下秀士, "Superspecial Trigonal Curves of Genus 5", 日本応用数理学会2018年年会 「数論アルゴリズムとその応用」(JANT) セッション, 名古屋大学, 2018, 2 pages (pdf).

19. 工藤桃成, 原下秀士, "種数4の超特別曲線を数え上げるアルゴリズムについて", Bulletin of the Japan Society for Symbolic and Algebraic Computations, Vol. 24, No. 2, pp. 43-46, 2018 (pdf).

20. 横田祐貴, 工藤桃成, 安田雅哉, "指数計算法による素体上のECDLP 解読の高速化", Bulletin of Japan Society for Symbolic and Algebraic Computations, Vol. 24, No. 2, pp. 35-38, 2018 (pdf).

21. 工藤桃成, "体上の楕円曲線の一般論", 第25回整数論サマースクール「楕円曲線とモジュラー形式の計算」報告集 (編: 木村巌, 横山俊一), pp. 11-41, 2018 (pdf). 

22. 横田祐貴, 高橋康, 工藤桃成, 安田雅哉, "素体上のECDLPに対するAlessandroらの指数計算法の高速化", 2018年暗号と情報セキュリティシンポジウム (SCIS2018), 3B3-2, 2018, 7 pages (pdf).

23. 工藤桃成, "グレブナー基底に基づく連接層係数コホモロジー群計算アルゴリズムの評価", Bulletin of Japan Society for Symbolic and Algebraic Computations, Vol. 23, No. 2, pp. 108-111, 2017 (pdf).

24. Momonari Kudo, "Attacks against search Poly-LWE", 2017年暗号と情報セキュリティシンポジウム (SCIS2017), 2B4-5, 2017, 8 pages (pdf).

25. 工藤桃成, "Magmaによるcoherent cohomologyの次元計算", RIMS講究録, Vol. 2012, pp. 81-93, 2016 (pdf).

26. Momonari Kudo, "High-speed computation of the dimensions of coherent cohomology by computer algebra systems", 11th Symposium on Algebra and Computation (AC2015), Tokyo Metropolitan University, 14-16th December 2015, pp. 179-191, 2016, available at http://jant.jsiam.org/ac/2015/ac2015_proceedings.pdf.

27. Momonari Kudo, Yang Guo and Masaya Yasuda, "Comparison of Babai's nearest plane and rounding algorithms in Laine-Lauter's key recovery attack for LWE", 2016年暗号と情報セキュリティシンポジウム (SCIS2016), 2D4-1, 2016, 8 pages (pdf).

28. Jintai Ding, Momonari Kudo, Shinya Okumura, Tsuyoshi Takagi and Chengdong Tao, "On the security of a public key cryptosystem based on diophantine equations of degree increasing type", 2016年暗号と情報セキュリティシンポジウム (SCIS2016), 1D2-3, 2016, 8 pages (pdf).