Workshop on Mathematics and Cryptography

Hyungrok Jo

Abstract. Classical discrete-logarithm-based cryptography has long served as a fertile substrate for advanced cryptographic primitives such as identity-based encryption, ring and threshold signatures, proxy re-encryption, broadcast schemes, and many more, built on the algebraic richness of cyclic groups and the conjectured hardness of the discrete logarithm and Diffie–Hellman problems. The transition to post-quantum cryptography, however, has so far been dominated by lattice- and code-based assumptions that do not naturally expose such a group structure, making advanced functionalities considerably more delicate to construct.
Isogeny-based cryptography offers a post-quantum analogue of the discrete-logarithm setting. Through the framework of cryptographic group actions, originally formalized by Couveignes and Rostovtsev–Stolbunov in 2006 and revitalized by CSIDH (Commutative Supersingular Isogeny Diffie–Hellman) in 2019, the vectorization and parallelization problems play the role of DL and CDH, respectively, providing a structural template for advanced post-quantum schemes. In this talk, we begin with a gentle tour from elliptic curves and isogenies to the abstract framework of effective group actions and hard homogeneous spaces, which is not affected by the 2022 attacks on SIDH. We then survey how this DLP analogue enables advanced post-quantum primitives such as ElGamal-like encryption, proxy re-encryption, and signatures, and conclude with open problems and research directions.

Bio. Hyungrok Jo is a Specially Appointed Assistant Professor at the Institute of Advanced Sciences, Yokohama National University, Japan, affiliated with Prof. Junji Shikata's laboratory since 2021. He received his Ph.D. in Mathematics from Kyushu University in 2017 under Prof. Tsuyoshi Takagi as a member of the JST CREST CryptoMathCREST project, and subsequently held a postdoctoral position at the University of Tsukuba from 2017 to 2021 under Prof. Noboru Kunihiro. His research centers on isogeny- and group-action-based post-quantum cryptography and its applications to advanced primitives, as well as graph-theoretic constructions of cryptographic hash functions. He serves as a board member of the Korea Institute of Information Security and Cryptology (KIISC).

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Yasuhiko Ikematsu

Abstract. It is believed that existing cryptosystems can be broken by Shor’s algorithm using a large-scale quantum computer.  Therefore, there is a need to develop cryptosystems resistant to quantum-computer attacks, known as post-quantum cryptography (PQC). Multivariate public-key cryptosystems (MPKC) are based on the hardness of solving systems of multivariate quadratic equations over a finite field, and are one of the main candidates for PQC. This talk introduces the basic construction and security analysis of MPKC, focusing on the UOV signature scheme, one of the leading multivariate signature schemes. It also explains several variants of UOV that advanced to the third round of the NIST PQC standardization process for additional digital signatures.

Bio. Yasuhiko Ikematsu received the PhD in mathematics in 2016 from Kyushu University. He was a research fellow in Institute of Mathematics for Industry, Kyushu University from 2016 to 2018 and in Department of Mathematical Informatics, University of Tokyo from April to December in 2018. He is currently an associate professor in Institute of Mathematics for Industry, Kyushu University.

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Tang Khai Hanh

Abstract. A string $\mathbf{s}$, dubbed keyword, is a subsequence of another string $\mathbf{t}$, dubbed text, if $\mathbf{s}$ can be obtained by deleting some characters from $\mathbf{t}$; otherwise, $\mathbf{s}$ is a non-subsequence of $\mathbf{t}$. (Non-)subsequence relationships arise in various fields, including genetic analysis, blockchains, and natural language processing. Recently, Ling et al. (SCN 2024) proposed a succinct argument for non-subsequences based on multivariate sumcheck (Lund et al., FOCS 1990) whose prover's running time is at least $\mathcal{O}(n + N + |\Sigma|)$, where $n$ and $N$ are respectively the lengths of strings $\mathbf{s}$ and $\mathbf{t}$, and $\Sigma$ is the alphabet over which $\mathbf{s}$ and $\mathbf{t}$ are defined. As shown in their work, proving non-subsequence relationships is non-trivial since one needs to decompose such an argument into smaller components for sumcheck, permutation, and lookup.

We propose a preprocessing-based SNARK for (non-)subsequences that separates the process of proving either subsequences or non-subsequences a subsequence scheme that separates the process of proving (non-)subsequences into the following two phases: (i) a preprocessing phase and (ii) a (non-)subsequence proving phase, assuming $n \ll N$ (i.e., $|\mathbf{s}| \ll |\mathbf{t}|$). Specifically, we can generate a one-time preprocessing proof with inputs $\mathbf{t}$ and $\Sigma$, without any knowledge of $\mathbf{s}$. When $\mathbf{s}$ is known, we can determine whether $\mathbf{s}$ is a subsequence of $\mathbf{t}$ and prove the corresponding statement. Employing cached quotients (IACR ePrint 2022/1763), we achieve a running time quasi-linear in $N + |\Sigma|$ for preprocessing, while the running time of proving a (non-)subsequence relationship is $\mathcal{O}(n \log_2 (N + |\Sigma|))$ for each query $\mathbf{s}$. Since $n \ll N$ and $\log_2(N + |\Sigma|)$ grows sub-linearly with the text size, this saves the prover's running time, assuming a preprocessing depending only on $\mathbf{t}$ is computed in advance. Hence, we achieve a text-sub-linear proving time.

Joint work with Dario Fiore, San Ling, Hong Hanh Tran, Huaxiong Wang, and Yingfei Yan. Accepted at ESORICS 2026; preprint available on ePrint (https://eprint.iacr.org/2026/008 ); proceedings version to appear.

Bio. Khai Hanh Tang is a Research Fellow at Nanyang Technological University (NTU), Singapore. He obtained his Ph.D. from NTU, Singapore, in 2022, and his B.Sc. from the University of Science, Vietnam National University Ho Chi Minh City (HCMUS-VNUHCM), in 2017. His research focuses on zero-knowledge proofs, SNARKs, and privacy-preserving digital signatures.

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Tran Ngo

Abstract. The Learning With Errors (LWE) problem, introduced by Regev (STOC’05), is one of the fundamental problems in lattice-based cryptography, believed to be hard even for quantum adversaries. Regev (FOCS’02) showed that LWE reduces to the quantum Dihedral Coset Problem (DCP). Later, Brakerski, Kirshanova, Stehlé and Wen (PKC’18) showed that LWE reduces to a generalization known as the Extrapolated Dihedral Coset Problem (EDCP). We present a quasi-polynomial time quantum algorithm for the EDCP problems over power-of-two moduli using a quasi-polynomial number of samples, which also applies to the SLWE problem defined by Chen, Liu, and Zhandry (Eurocrypt’22). Our EDCP algorithm can be viewed as a provable variant to the “Simon-meets-Kuperberg” algorithm introduced by Bonnetain and Naya-Plasencia (Asiacrypt’18), adapted to the EDCP setting. We stress that our algorithm does not affect the security of LWE with standard parameters, as the reduction from standard LWE to EDCP limits the number of samples to be polynomial.

Bio.

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Chi Do

Abstract. Anamorphism [EC 22] embeds a hidden communication channel for the members of a ring of users within a hosting cryptographic primitive. The channel remains hidden even to the eyes of a dictator who can force disclosure of all the secret keys (whose existence could not be denied). Since various authorities resistance and actions against having strong crytography have been persistence globally (a phenomenon known as the “crypto war”), anamorphism, being a tool against the crypto war, is an important research aspect of current cryptography. Here we consider Key Encapsulation Mechanisms (KEMs) as the hosting primitive, and investigate the construction of Asymmetric and Robust Anamorphism: that is, a KEM that hosts a covert secure encryption scheme that, besides the basic anamorphic guaranties, ensures that messages remain secret even if members of the ring are corrupted (a notion considered in [PoPETS 23 and CRYPTO 24]), and that successfully decrypted messages originate from within the ring (a notion considered under the name “robustness” in a weaker form in [EC 24]).We propose a new general technique we call “Broadcast in the Head (BitH),” for constructing anamorphic KEM schemes by leveraging Anonymous Broadcast Encryption (Anon BE). The core of our approach is a method allowing a sender to embed a multi-bit (anamorphic) message into a virtual target set (shadow receivers), where each shadow recipient can recover individual bits of the message. Our construction supports messages significantly longer than that in the previous work. We apply our generic technique to show that the Dual Regev (DR) KEM scheme [STOC 08] is multi-bit anamorphic by giving two instantiations of the BitH technique. In our first construction, we obtain multi-bit asymmetric and robust anamorphism for DR. The construction exploits error-correcting codes for a specific channel (the Z-channel) that arises in the decryption process of Anon BE. As a byproduct, if we coalesce the regular and the anamorphic receiver into a single receiver, we increase the single-bit capacity of DR and achieve multi-bit DR-like public-key encryption with the same ciphertext size as the original DR, at the expense of larger keys; (in fact, we believe the message extension technique tradeoff may be of interest, independently of anamorphism). In the second construction, we obtain robust anamorphism for DR. This construction is more efficient as it does not use error-correcting codes but this efficiency comes at the cost of losing the asymmetric anamorphism property.

Bio.

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Hieu Van Ha

Abstract. In this talk, I will provide a gentle introduction to the fundamental concepts of algebraic coding theory, with a particular emphasis on cyclic codes and constacyclic codes, which form two of the most widely studied families of linear codes due to their rich algebraic structure and efficient encoding and decoding algorithms. I will begin by briefly recalling the motivation behind error-correcting codes and how algebraic tools—especially polynomial representations over finite fields—allow us to analyze and construct such codes in a systematic way. I will then focus on the Hamming distance of constacyclic codes, discussing how it determines the error-detecting and error-correcting capability of a code. In particular, I will explain the role of the Singleton bound, a fundamental upper bound on the minimum distance of a code, and show how it is used to characterize MDS (maximum distance separable) and AMDS (almost MDS) codes utilizing from repeated-root constacyclic codes. In the final part of the talk, I will move beyond the classical Hamming metric and introduce the notion of symbol-pair distance, which arises in the context of channels where symbols are read in overlapping pairs rather than individually—such as in high-density storage systems. I will explain how this new metric changes the design criteria for optimal codes and present some recent constructions of optimal cyclic codes with respect to the symbol-pair distance.

Bio. Hieu V. Ha is a Lecturer at the University of Economics and Law, VNU-HCM. He received his B.Sc. in Mathematics from Ho Chi Minh City University of Education in 2010, his M.Sc. in Mathematics from University of Bordeaux in 2013, and his Ph.D. in Mathematics from University of Galway in 2019. His research interests focus on algebraic coding theory, matrix theory, and Lie algebras. Since his undergraduate studies, he has concentrated on algebraic structures over finite fields and their applications. His undergraduate research concerned the classification of Lie algebras, while his master’s thesis studied L-functions of algebraic curves over finite fields. He obtained his Ph.D. in Mathematics at the University of Galway under the supervision of Rachel Quinlan, with a dissertation entitled Entry Pattern Matrices.

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Dinh Van Hoang

Abstract.The classical Noether Normalization Lemma states that if S is a finitely generated algebra over a field k, then there exist elements x1, . . . , xn which are algebraically independent over k such that S is a finite module over k[x1, . . . , xn]. This lemma has been studied intensively in different flavors. In 2024, Elad Paran and Thieu N. Vo successfully generalized this lemma for the case when S is a quotient ring of the skew polynomial ring D[x1, . . . , xn; σ1, . . . , σn]. In this paper, we investigate this lemma in a more general setting when S is a quotient ring of an iterated skew polynomial ring D[x1; σ1, δ1] . . . [xn; σn, δn]. We extend several key results of Elad Paran and Thieu N. Vo to this broader context and introduce a new version of Combinatorial Nullstellensatz over division rings.

Bio. Dinh Van Hoang earned his Bachelor’s and Master’s degrees in Mathematics from Ho Chi Minh City University of Science in 2004 and 2008, respectively. He obtained his Ph.D. in Mathematics from the University of Antwerp, Belgium, in 2016. His research centers on Algebraic Geometry, Deformation theory and related topics. From 2017 to 2020, he served as a lecturer and researcher in Mathematics at the Faculty of Applied Sciences, Ho Chi Minh City University of Technology and Engineers (HCMUTE). Since 2021, he has been a faculty member at the Faculty of Advanced Education, HCMUTE.

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Dang Tuan Hiep

Abstract. This talk discusses the geometry of Newton polytopes associated with homogenized symmetric polynomials. We describe how homogenization produces a layered polyhedral structure from the homogeneous components of a symmetric polynomial. We further explain connections with saturated Newton polytopes (SNP), generalized permutahedron, and M-convexity in discrete convex analysis. Examples from Schur and Grothendieck polynomials are also presented.

Bio. Dang Tuan Hiep is an Associate Professor of Mathematics at Dalat University. He received his Ph.D. in Mathematics from University of Kaiserslautern and was a postdoctoral researcher at National Taiwan University. His research interests include Algebraic Geometry, Algebraic Combinatorics, Schubert calculus, and Computer Algebra, with contributions to Newton polytopes, Grothendieck polynomials, Grassmannians, and discrete convex analysis. He is also developing computational packages for Schubert calculus in Julia/Oscar and is interested in applications of mathematics to data science, finance, and biology.

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Nguyen Duy Tung Khanh

Abstract. Cloud computing and outsourced computation have fundamentally transformed the way modern systems store data and execute large-scale computations. By delegating computation to external servers, users gain scalability and efficiency, but also introduce critical concerns regarding security, privacy, and trustworthiness. How can users ensure that sensitive data remains private? How can they verify that an untrusted cloud server performs computations correctly? And how can these guarantees be achieved efficiently in practice?

This talk provides an overview of the fundamental challenges and modern cryptographic approaches for trustworthy outsourced computation. We first discuss the threat model and trust assumptions in cloud environments, followed by key techniques including homomorphic encryption, secure multi-party computation, and verifiable computation. We then examine the trade-offs between security guarantees, computational overhead, and practical deployment. Finally, we highlight emerging research directions in trustworthy outsourced computation.

Bio. Khanh Nguyen received his Bachelor degree from Le Quy Don University and his PhD from the Institute of Cybersecurity and Cryptology at the University of Wollongong, Australia. His research interests include privacy enhancing technologies, applied cryptography, and the security of information systems.

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Dung Duong

Abstract. This talk gives an accessible introduction to cryptographic group actions and how they support modern post-quantum constructions. After a brief overview of the basic definitions and the core security intuition—what is easy to compute, what is believed to be hard, and why the group-action viewpoint is useful—I will survey a few recent protocols built from group actions, highlighting the main design ideas and the practical obstacles that keep appearing across schemes, and conclude with some interesting directions and open problems.

Bio. Dung Duong received his PhD in Mathematics from Leiden University in 2013. Upon completion of his doctoral studies, he undertook a postdoctoral research appointment in the Faculty of Mathematics at Bielefeld University, where he was affiliated from 2013 to 2015. Subsequently, he was appointed Assistant Professor at the Institute of Mathematics for Industry, Kyushu University, a position he held from 2015 to 2018. Since 2018, Duong has been serving as a Senior Lecturer in the School of Computing and Information Technology at the University of Wollongong. His research interests lie primarily in post‑quantum cryptography, with a focus on the theoretical foundations and practical development of cryptographic systems resilient to quantum computational attacks.

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