TODO
Reading queue: AO primitive designs
- Grassi et al. "Poseidon: A New Hash Function for Zero-Knowledge Proof Systems" ePrint 2019/458
- Grassi et al. "Poseidon2: A Faster Version of the Poseidon Hash Function" ePrint 2023/323
- Bouvier et al. "Anemoi Permutations and Jive Compression Mode" ePrint 2022/840
- Grassi et al. "Horst Meets Fluid-SPN: Griffin" ePrint 2022/403
- Aly et al. "Efficient Symmetric Primitives for Advanced Cryptographic Protocols" (Rescue/Vision/etc.) ePrint 2020/1143
- Grassi et al. "Reinforced Concrete" ePrint 2021/1038
- Grassi, Khovratovich, Luftenegger, Rechberger, Schofnegger, Walch. "Monolith: Circuit-Friendly Hash Functions with New Nonlinear Layers for Fast and Constant-Time Implementations" ePrint 2023/1025
- Szepieniec. "The Tip5 Hash Function for Recursive STARKs" ePrint 2023/107
- Bouvier, Grassi, Khovratovich, Koschatko, Rechberger, Schmid, Schofnegger. "Skyscraper-v2: Fast Hashing on Big Primes" ePrint 2025/058
- Ha, Hwang, Lee, Park, Son. "Polocolo: A ZK-Friendly Hash Function Based on S-boxes Using Power Residues" (EUROCRYPT 2025) ePrint 2025/926
- Grassi et al. "Poseidon(2)b: Binary Field Versions of Poseidon/Poseidon2" ePrint 2025/1893
- Ashur, Mahzoun, Posen, Sijacic. "Vision Mark-32: ZK-Friendly Hash Function Over Binary Tower Fields" ePrint 2024/633
- Ashur, Tariq. "RPO-M31 and XHash-M31: Efficient Hash Functions for Circle STARKs" ePrint 2024/1635
- Ashur, Al Kindi. "Arithmetization Oriented Encryption" (AEAD via MonkeySpongeWrap + RPO) ePrint 2023/1668
- Feneuil, Rivain. "CAPSS: A Framework for SNARK-Friendly Post-Quantum Signatures" ePrint 2025/061
- Duzyol, Otal. "Leveraging Smaller Finite Fields for More Efficient ZK-Friendly Hash Functions" ePrint 2025/1593
- Adomnicai. "Towards Practical Multi-Party Hash Chains using AO Primitives - With Applications to Threshold Hash-Based Signatures" ePrint 2025/2290
- Albrecht, Grassi, Rechberger, Roy, Tiessen. "MiMC: Efficient Encryption and Cryptographic Hashing with Minimal Multiplicative Complexity" (ASIACRYPT 2016) ePrint 2016/492
- Albrecht, Grassi, Perrin, Ramacher, Rechberger, Rotaru, Roy, Schofnegger. "Feistel Structures for MPC, and More" (GMiMC, ESORICS 2019) ePrint 2019/397
- Grassi, Luftenegger, Rechberger, Rotaru, Schofnegger. "On a Generalization of Substitution-Permutation Networks: The HADES Design Strategy" ePrint 2019/1107
- Grassi, Luftenegger, Rechberger, Rotaru, Schofnegger. "Mind the Middle Layer: The HADES Design Strategy Revisited" ePrint 2020/179
- Ashur, Dhooghe. "MARVELlous: a STARK-Friendly Family of Cryptographic Primitives" (Jarvis, Friday, Vision, Rescue) ePrint 2018/1098
- Ashur, Mahzoun, Posen, Willems. "Rescue-Prime Optimized" (RPO) ePrint 2022/1577
- Ashur, Bhati, Al Kindi, Mahzoun, Perrin. "XHash: Efficient STARK-friendly Hash Function" ePrint 2023/1045
- Dobraunig, Grassi, Guinet, Kuijsters. "Ciminion: Symmetric Encryption Based on Toffoli-Gates over Large Finite Fields" (EUROCRYPT 2021) ePrint 2021/267
- Grassi, Oygarden, Schofnegger, Walch. "From Farfalle to Megafono via Ciminion: The PRF Hydra for MPC Applications" (EUROCRYPT 2023) ePrint 2022/342
- Dobraunig, Kales, Rechberger, Schofnegger, Zaverucha. "Shorter Signatures Based on Tailor-Made Minimalist Symmetric-Key Crypto" (RAIN/Rainier, CCS 2022) ePrint 2021/692
- Kim, Ha, Son, Lee, Moon, Lee, Lee, Kwon, Cho, Yoon, Cho. "AIM: Symmetric Primitive for Shorter Signatures with Stronger Security" (AIMer, CCS 2023) ePrint 2022/1387
- Szepieniec. "On the Use of the Legendre Symbol in Symmetric Cipher Design" (Grendel) ePrint 2021/984
- Roy, Steiner et al. "Arion: Arithmetization-Oriented Permutation and Hashing from Generalized Triangular Dynamical Systems" arXiv 2303.04639
- Bettale, Kahrobaei, Perret, Verbel. "Biscuit: New MPCitH Signature Scheme from Structured Multivariate Polynomials" ePrint 2023/1760
Reading queue: algebraic VDFs
- Lenstra, Wesolowski. "A random zoo: sloth, unicorn, and trx" (Sloth, foundational slow-hash VDF) ePrint 2015/366
- Khovratovich, Maller, Tiwari. "MinRoot: Candidate Sequential Function for Ethereum VDF" ePrint 2022/1626
Reading queue: AO primitive signatures (Legendre/Power-Residue PRF)
- Loquat group. "Loquat: A SNARK-Friendly Post-Quantum Signature based on the Legendre PRF" (Crypto 2024) ePrint 2024/868
- Zhang, Li, Steinfeld, Zhao, Liu, Yuen. "Pegasus and PegaRing: Efficient (Ring) Signatures from Sigma-Protocols for Power Residue PRFs" ePrint 2025/1841
Reading queue: cryptanalysis of AO primitives
- Bariant, Peyrin. "Algebraic Attacks against Some AO Primitives" (2022)
- Keller, Rosemarin. "STARK Friendly Hash Survey" (2020)
- Bariant, Boeuf, Briaud, Hostettler, Oygarden, Raddum. "Improved Resultant Attack against Arithmetization-Oriented Primitives" ePrint 2025/259
- Yang, Zheng, Yang, Liu, Tang. "A New Security Evaluation Method Based on Resultant for Arithmetic-Oriented Algorithms" ePrint 2024/886
- Steiner. "Zero-Dimensional Groebner Bases for Rescue-XLIX" ePrint 2024/468
- Ashur, Buschman, Mahzoun. "Algebraic Cryptanalysis of HADES Design Strategy: Application to POSEIDON and Poseidon2" ePrint 2023/537
- Sun, Chen, Liu, Wang, Niu. "High Exponents May Not Suffice to Patch AIM (On Attacks, Weak Parameters, and Patches for AIM2)" ePrint 2025/2272
- Sanso, Vitto. "Attacking Poseidon via Graeffe-Based Root-Finding over NTT-Friendly Fields" ePrint 2025/937
- Zhao, Ding. "Breaking Poseidon Challenges with Graeffe Transforms and Complexity Analysis by FFT Lower Bounds" ePrint 2025/950
- Grassi, Koschatko, Rechberger. "Poseidon and Neptune: Groebner Basis Cryptanalysis Exploiting Subspace Trails" ePrint 2025/954
- Zhao, Sanso, Vitto, Ding. "Graeffe-Based Attacks on Poseidon and NTT Lower Bounds" ePrint 2025/1916
- Bak, Bariant, Boeuf, Briaud, Oygarden, Phanse. "The Algebraic CheapLunch: Extending FreeLunch Attacks on AO Primitives Beyond CICO-1" ePrint 2025/2040
- Yang, Zheng, Yang. "Algebraic Cryptanalysis of AO Primitives Based on Polynomial Decomposition: Applications to Rain and Full AIM-III/IV" ePrint 2025/981
- Campa, Roy. "Groebner Basis Cryptanalysis of Anemoi" ePrint 2025/814
- Chang, Qiao, Cheng, Ou, Zhu. "Programming Equation Systems of AO Primitives with Constraints" ePrint 2024/2061
- Liu, Mahzoun, Meier. "Modelling Ciphers with Overdefined Systems of Quadratic Equations: Application to Friday, Vision, RAIN and Biscuit" ePrint 2024/786
- Bariant, Boeuf, Lemoine, Manterola Ayala, Oygarden, Perrin, Raddum. "The Algebraic FreeLunch: Efficient Groebner Basis Attacks Against Arithmetization-Oriented Primitives" (Crypto 2024) ePrint 2024/347
- Koschatko, Luftenegger, Rechberger. "Exploring the Six Worlds of Groebner Basis Cryptanalysis: Application to Anemoi" (ToSC 2024/4) ePrint 2024/250
- Briaud. "A Note on Groebner Bases for Anemoi" (withdrawn April 2025) ePrint 2024/693
- Koschatko et al. "Opening the Blackbox: Collision Attacks on Round-Reduced Tip5, Tip4, Tip4' and Monolith" (ToSC 2024/4) ePrint 2024/1900
- Bak. "A Practical Distinguisher on the Full Skyscraper Permutation" ePrint 2025/102
- Liu, Mahzoun, Oygarden, Meier. "Algebraic Attacks on RAIN and AIM Using Equivalent Representations" (ToSC 2023/4) ePrint 2023/1133
- Zhang et al. "Algebraic Attacks on Round-Reduced RAIN and Full AIM-III" ePrint 2023/1397
- Bariant. "A Univariate Attack against Ciminion in the Limited-Data Regime" ePrint 2023/1283
- Steiner. "Groebner Basis Cryptanalysis of Ciminion and Hydra" (ToSC 2025/1)
- Bak, Perrin. "On the Security of Split-and-Lookup-Based ZK-Friendly Primitives" (ToSC 2025/2)
- Bak, Jazeron, Galissant, Perrin. "Attacking Split-and-Lookup-Based Primitives Using Probabilistic Polynomial System Solving: Applications to Round-Reduced Monolith and Full-Round Skyscraper" (ToSC 2025/3)
- Hovhannisyan, Asaturyan, Hovhannisyan. "Cryptanalysis of Poseidon-Based Fiat-Shamir Protocols" ePrint 2026/409
- Bak, Bariant, Boeuf, Hostettler, Jazeron. "Claiming Bounties on Small Scale Poseidon and Poseidon2 Instances Using Resultant-Based Algebraic Attacks" ePrint 2026/150
- Merz, Rodriguez Garcia. "Skipping Class: Algebraic Attacks Exploiting Weak Matrices and Operation Modes of Poseidon2(b)" ePrint 2026/306
- Biryukov, Fisch, Herold, Khovratovich, Leurent, Naya-Plasencia, Wesolowski. "Cryptanalysis of Algebraic Verifiable Delay Functions" (Crypto 2024, analyzes Sloth++/Veedo/MinRoot) ePrint 2024/873
Reading queue: security proofs and frameworks for AO
- Boeuf, Perrin. "ALFOMs and the Moirai: Quantifying the Performance/Security Tradeoff for ZK-friendly Hash Functions" ePrint 2025/1920
- Andreeva, Bhattacharyya, Roy, Trevisani. "On Efficient and Secure Compression Modes for Arithmetization-Oriented Hashing" (IEEE CSF 2024) ePrint 2024/047
- Guo, Hu, Jiang, Fan, Fu, Preneel, Wang. "Permutation-Based Hash from Non-Idealized Assumptions: Adding Feed-Forward to Sponge" (SpongeFwd) ePrint 2025/1006
- Ozdemir, Pailoor, Bassa, Ferles, Barrett, Dillig. "Split Groebner Bases for Satisfiability Modulo Finite Fields" (CAV 2024) ePrint 2024/572
Reading queue: Groebner bases, computational algebra, finite fields
Textbooks
- Cox, Little, O'Shea. "Ideals, Varieties, and Algorithms" (4th ed., Springer 2015). The standard introduction to Groebner bases, Buchberger's algorithm, elimination theory, resultants, Nullstellensatz.
- Cox, Little, O'Shea. "Using Algebraic Geometry" (2nd ed., Springer 2005). Sequel: resultants, syzygies, Hilbert functions, coding theory.
- Adams, Loustaunau. "An Introduction to Groebner Bases" (AMS GSM Vol. 3, 1994). Concise graduate-level treatment of Groebner bases.
- Becker, Weispfenning. "Groebner Bases: A Computational Approach to Commutative Algebra" (Springer, 1993). Rigorous treatment with detailed proofs and term orderings.
- Kreuzer, Robbiano. "Computational Commutative Algebra 1 and 2" (Springer, 2000/2005). Theory + computation with CoCoA system.
- Lidl, Niederreiter. "Finite Fields" (CUP, 2nd ed., 1997). The comprehensive reference on finite field theory, polynomial arithmetic over GF(p) and GF(p^n), factorization algorithms.
- Lidl, Niederreiter. "Introduction to Finite Fields and Their Applications" (CUP, revised ed., 1994). Accessible version of the above.
- von zur Gathen, Gerhard. "Modern Computer Algebra" (CUP, 3rd ed., 2013). Algorithms for polynomial arithmetic, GCD, factorization, resultants, modular methods.
- Bard. "Algebraic Cryptanalysis" (Springer, 2009). The only textbook-length treatment: modeling ciphers as polynomial systems, finite field linear algebra, solving methods (SAT, Groebner, XL).
- Joux. "Algorithmic Cryptanalysis" (CRC Press, 2009). Broader scope including algebraic methods, Groebner bases, lattice techniques.
- Ding, Petzoldt, Schmidt. "Multivariate Public Key Cryptosystems" (Springer, 2nd ed., 2020). MQ problem, HFE, UOV, Rainbow, solving algorithms over finite fields.
Key papers: Groebner basis algorithms
- Faugere. "A New Efficient Algorithm for Computing Groebner Bases (F4)" (J. Pure Appl. Algebra, 1999). Parallel reductions via sparse matrix linear algebra.
- Faugere. "A New Efficient Algorithm for Computing Groebner Bases without Reduction to Zero (F5)" (ISSAC 2002). Signature-based criteria to avoid redundant reductions. State of the art.
- Lazard. "Resolution des Systemes d'Equations Algebriques" (TCS, 1981). Connects Groebner bases to Macaulay matrices. Lazard/Macaulay bound.
- Lazard. "Groebner Bases, Gaussian Elimination and Resolution of Systems of Algebraic Equations" (EUROCAL 83). GB computation as generalized Gaussian elimination.
Key papers: semi-regularity, degree of regularity, complexity
- Bardet, Faugere, Salvy. "On the Complexity of Groebner Basis Computation of Semi-Regular Overdetermined Algebraic Equations" (ICPSS 2004). Defines semi-regular sequences, D_reg, sharp asymptotic complexity. Basis for most multivariate security analyses.
- Bardet, Faugere, Salvy. "Complexity of Groebner Basis Computation for Semi-Regular Overdetermined Sequences over F_2" (INRIA RR-5049, 2003). Boolean specialization of the above.
- Bardet, Faugere, Salvy. "On the Complexity of the F5 Groebner Basis Algorithm" (J. Symbolic Computation, 2015). Refined F5 complexity bounds. arXiv:1312.1655
- Ding, Hodges. "Solving Degree and Degree of Regularity for Polynomial Systems over Finite Fields" (SAC 2013). Clarifies when D_reg gives valid security estimates.
- Caminata, Gorla. "Solving Degree, Last Fall Degree, and Related Invariants" (J. Symbolic Computation, 2023). Rigorous framework relating solving degree, first/last fall degree, D_reg, Castelnuovo-Mumford regularity. ePrint 2021/1611
- Caminata, Gorla. "On Hilbert-Poincare Series of Affine Semi-Regular Polynomial Sequences and Related Groebner Bases" (2024). Hilbert series for inhomogeneous semi-regular systems (closer to crypto setting). ePrint 2024/086
Key papers: XL algorithm and hybrid approaches
- Courtois, Klimov, Patarin, Shamir. "Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations" (Eurocrypt 2000). Introduces XL algorithm for overdetermined MQ systems.
- Ars, Faugere, Imai, Kawazoe, Sugita. "Comparison Between XL and Groebner Basis Algorithms" (Asiacrypt 2004). Proves XL is a redundant variant of F4.
- Bettale, Faugere, Perret. "Hybrid Approach for Solving Multivariate Systems over Finite Fields" (J. Math. Cryptology, 2009). Combines exhaustive search + Groebner computation.
Key papers: algebraic cryptanalysis of symmetric primitives
- Courtois, Pieprzyk. "Cryptanalysis of Block Ciphers with Overdefined Systems of Equations" (Asiacrypt 2002). Founded algebraic cryptanalysis of block ciphers (AES/Serpent as polynomial systems). ePrint 2002/044
- Buchmann, Pyshkin, Weinmann. "Block Ciphers: Algebraic Cryptanalysis and Groebner Bases" (in Sala et al., Springer, 2009). Survey of GB-based cryptanalysis of block ciphers.
Coauthor analysis
- List all coauthors across all AO primitives papers (design and cryptanalysis). Map out who has worked on what, and investigate their other publications. Useful for understanding the research landscape, finding related work, and identifying key contributors to the field.
Author directory
Researchers appearing across the papers above, grouped by primary field.
AO primitive designers
| Name | Affiliation | Field |
|---|---|---|
| Lorenzo Grassi | Ruhr University Bochum | Symmetric crypto, AO design (Poseidon, Poseidon2, Griffin, Reinforced Concrete, Monolith, Skyscraper) |
| Dmitry Khovratovich | Ethereum Foundation | Symmetric crypto, hash design, memory-hard functions (Argon2) |
| Christian Rechberger | TU Graz | Symmetric crypto, privacy-preserving computation, AO design |
| Clemence Bouvier | Inria Paris / Sorbonne | Symmetric crypto, algebraic cryptanalysis, AO design (Anemoi, Skyscraper) |
| Charalambos Chaidos | Univ. of Athens / UCL | Zero-knowledge proofs, SNARKs, blockchain protocols |
| Robin Salen | Polygon Zero | ZK proofs, ZK-friendly hashing, Plonky ecosystem |
| Vesselin Velichkov | Univ. of Edinburgh | Symmetric crypto, differential cryptanalysis, automated tools |
| Danny Willems | o1Labs (Mina) | ZK proofs, elliptic curves, proof systems engineering |
| Reinhard Luftenegger | Shielded Technologies | AO primitive analysis, ZK-friendly crypto (PhD: "Algebraic Analysis of AO Primitives") |
| Markus Schofnegger | Horizen Labs | ZK proofs, ZK-friendly hash functions |
| Roman Walch | TU Graz | Symmetric crypto (Monolith co-author) |
| Fabian Schmid | TU Graz | Symmetric crypto (Skyscraper-v2 co-author) |
| Tomer Ashur | 3MI Labs (prev. TU Eindhoven, KU Leuven) | Symmetric crypto design (Rescue, Vision, RPO-M31, XHash) |
| Alan Szepieniec | Neptune Cash / Triton Software | Post-quantum crypto, STARKs, Tip5 designer |
| Jincheol Ha | KAIST | Symmetric crypto (Polocolo co-author) |
| Seongha Hwang | KAIST | Symmetric crypto (Polocolo co-author) |
| Jooyoung Lee | KAIST | Symmetric crypto (Polocolo co-author) |
| Seungmin Park | KAIST | Symmetric crypto (Polocolo co-author) |
| Mincheol Son | KAIST | Symmetric crypto (Polocolo co-author) |
| Al Kindi | Polygon | AO encryption (MonkeySpongeWrap + RPO) |
| Gokce Duzyol | Bogazici University | ZK-friendly hash functions, finite fields |
| Kamil Otal | TUBITAK BILGEM | Symmetric crypto, coding theory |
| Alexandre Adomnicai | prev. CryptoNext / NTU Singapore | Crypto engineering, lightweight crypto, efficient implementations |
| Martin Albrecht | King's College London / SandboxAQ | Computational algebra, lattice crypto, AO design (MiMC) |
| Siemen Dhooghe | KU Leuven (COSIC) | Symmetric crypto (MARVELlous: Jarvis, Friday, Vision, Rescue) |
| Amit Singh Bhati | KU Leuven (COSIC) | Symmetric crypto (XHash co-author) |
| Christoph Dobraunig | Intel Labs / TU Graz | Symmetric crypto (Ciminion, RAIN/Rainier, ASCON) |
| Anna Guinet | (Ciminion co-author) | AO cipher design |
| Daniel Kuijsters | (Ciminion co-author) | AO cipher design |
| Daniel Kales | TU Graz | Post-quantum signatures (RAIN/Rainier) |
| Greg Zaverucha | Microsoft Research | Post-quantum signatures (RAIN/Rainier, Picnic) |
| Dragos Rotaru | NordVPN / prev. KU Leuven | MPC, HADES design strategy, GMiMC |
| Sebastian Ramacher | AIT Austrian Inst. of Technology | MPC-friendly crypto (GMiMC) |
| Tyge Tiessen | prev. DTU Denmark | Symmetric crypto (MiMC co-author) |
| Seongkwang Kim | Samsung SDS | AIM/AIMer designer |
| Byeonghak Lee | Samsung SDS | AIM/AIMer designer |
| Dukjae Moon | Samsung SDS | AIM/AIMer designer |
| Sangyup Lee | Samsung SDS | AIM/AIMer designer |
| Jihoon Kwon | Samsung SDS | AIM/AIMer designer |
| Jihoon Cho | Samsung SDS | AIM/AIMer designer |
| Hyojin Yoon | Samsung SDS | AIM/AIMer designer |
| Joungmo Cho | Samsung SDS | AIM/AIMer designer |
| Mary Maller | Ethereum Foundation / PQShield | Crypto (MinRoot VDF co-author) |
| Pratyush Ranjan Tiwari | Johns Hopkins / prev. KU Leuven | Crypto (MinRoot VDF co-author) |
| Arjen K. Lenstra | EPFL | Computational number theory (Sloth VDF) |
AO cryptanalysts (algebraic attacks, Groebner bases)
| Name | Affiliation | Field |
|---|---|---|
| Augustin Bariant | Inria Paris (COSMIQ) | Algebraic cryptanalysis, differential crypto, AO attacks |
| Pierre Briaud | Inria Paris (COSMIQ) | Algebraic cryptanalysis, multivariate crypto, Groebner bases |
| Leo Perrin | Inria Paris | Symmetric crypto, S-box analysis, Boolean functions |
| Aurelien Boeuf | Inria Paris / ENS | Algebraic cryptanalysis, AO security metrics (ALFOMs) |
| Morten Oygarden | Simula UiB | Algebraic cryptanalysis, Boolean functions, Groebner bases |
| Havard Raddum | Simula UiB | Algebraic cryptanalysis |
| Antoine Bak | Inria Paris | Algebraic attacks on AO primitives (FreeLunch, CheapLunch, Skyscraper) |
| Guilhem Jazeron | Inria Paris (COSMIQ) | Algebraic attacks on ZK-friendly primitives |
| Pierre Galissant | Inria Paris (post-doc) | White-box crypto, algebraic constructions |
| Axel Lemoine | Inria / DGA (French MoD) | Algebraic cryptanalysis, Groebner basis attacks |
| Irati Manterola Ayala | Simula UiB / Univ. Bergen | Algebraic attacks on AO primitives |
| Atharva Phanse | Simula UiB | Symmetric crypto, cryptanalysis |
| Mael Hostettler | Telecom SudParis (IP Paris) | Algebraic cryptanalysis, resultant attacks on AO |
| Katharina Koschatko | TU Graz | Algebraic cryptanalysis, "Six Worlds" GB framework |
| Luca Campa | Univ. of Innsbruck | GB cryptanalysis, algebraic geometry applied to crypto |
| Arnab Roy | Univ. of Innsbruck | Symmetric crypto design/analysis, algebraic number theory |
| Matthias Johann Steiner | Univ. of Klagenfurt | Algebraic analysis of AO primitives (Rescue, Ciminion, Hydra) |
| Antonio Sanso | Ethereum Foundation | Applied crypto, Graeffe-based attacks on Poseidon |
| Giuseppe Vitto | Ethereum Foundation | ZK-friendly hashing, Graeffe-based attacks |
| Ziyu Zhao | Tsinghua University (YMSC) | Lattice crypto, Graeffe/FFT attacks on Poseidon |
| Jintai Ding | XJTLU / Univ. Cincinnati (emeritus) | Post-quantum crypto (ML-KEM/Kyber co-designer) |
| Thomas Peyrin | NTU Singapore | Symmetric crypto design and cryptanalysis |
| Nathan Keller | Bar-Ilan University | Symmetric cryptanalysis, combinatorics |
| Asaf Rosemarin | Bar-Ilan University | Symmetric cryptanalysis (HADES/Poseidon analysis) |
| Fukang Liu | Institute of Science Tokyo | Symmetric cryptanalysis (SHA-256 collision, AO attacks) |
| Mohammad Mahzoun | TU Eindhoven / 3MI Labs | Cryptanalysis of symmetric primitives, FHE-friendly ciphers |
| Willi Meier | FHNW Switzerland | Symmetric crypto, stream ciphers (ASCON co-designer) |
| Thomas Buschman | TU Eindhoven | Algebraic cryptanalysis (HADES/Poseidon) |
| Hong-Sen Yang | PLA Info. Engineering Univ. | Algebraic cryptanalysis, polynomial decomposition attacks |
| Qun-Xiong Zheng | PLA Info. Engineering Univ. | Algebraic cryptanalysis, AO security evaluation |
| Jing Yang | PLA Info. Engineering Univ. | Symmetric cryptanalysis (linear, algebraic) |
| Mengyu Chang | Beijing Institute of Technology | Algebraic cryptanalysis, equation systems for AO |
| Kexin Qiao | Beijing Institute of Technology | Symmetric cryptanalysis (differential, MILP), AO attacks |
| Simon-Philipp Merz | ETH Zurich | Post-quantum crypto, Poseidon2(b) attacks |
| Alex Rodriguez Garcia | UPC Barcelona | ZK proofs, Poseidon2(b) attacks |
| Kaiyi Zhang | Shanghai Jiao Tong Univ. | Algebraic attacks (RAIN, AIM-III) |
| Qingju Wang | Univ. of Luxembourg | Symmetric cryptanalysis |
| Yu Yu | Shanghai Jiao Tong Univ. | Foundations of crypto |
| Hongrui Cui | Shanghai Jiao Tong Univ. | Algebraic attacks |
| Yimeng Sun | Shandong University | AIM analysis |
| Shiyao Chen | Shandong University | AO cryptanalysis (AIM, Tip5/Monolith collisions) |
| Guowei Liu | Shandong University | AIM analysis |
| Meiqin Wang | Shandong University | Symmetric cryptanalysis |
| Chao Niu | Ant Group | AIM analysis |
| Hailun Yan | (Tip5/Monolith collisions co-author) | Symmetric cryptanalysis |
| Subhadeep Banik | (Tip5/Monolith collisions co-author) | Lightweight crypto, side-channel |
AO cryptanalysts (VDF, Fiat-Shamir)
| Name | Affiliation | Field |
|---|---|---|
| Alex Biryukov | Univ. of Luxembourg (CryptoLUX) | Applied crypto, cryptanalysis (Argon2 co-designer) |
| Ben Fisch | Yale / Espresso Systems | Applied crypto, verifiable computation |
| Gottfried Herold | Ruhr University Bochum | Public-key crypto, FHE |
| Gaetan Leurent | Inria Paris (COSMIQ) | Symmetric crypto, block cipher/hash cryptanalysis |
| Maria Naya-Plasencia | Inria Paris (COSMIQ) | Symmetric crypto, post-quantum symmetric security |
| Benjamin Wesolowski | CNRS / ENS Lyon | Number-theoretic crypto, isogenies (IACR Secretary) |
| Hayk Hovhannisyan | Yerevan State University | Poseidon-based Fiat-Shamir cryptanalysis |
| Nerses Asaturyan | Yerevan State Univ. / Layerswap Labs | Poseidon-based Fiat-Shamir cryptanalysis |
| Gohar Hovhannisyan | Yerevan State University | Poseidon-based Fiat-Shamir cryptanalysis |
Security proofs and frameworks
| Name | Affiliation | Field |
|---|---|---|
| Elena Andreeva | TU Wien | Symmetric authenticated encryption, AO hashing modes |
| Rishiraj Bhattacharyya | Univ. of Birmingham | Cryptographic hash functions, provable security |
| Stefano Trevisani | (AO compression modes co-author) | Provable security |
| Chun Guo | Shandong University | Provable security, SpongeFwd |
| Kai Hu | Shandong University | Provable security, SpongeFwd |
| Bart Preneel | KU Leuven (COSIC) | Symmetric crypto, hash functions |
| Alex Ozdemir | Stanford | Formal verification, SMT for finite fields |
| Alp Bassa | Veridise | Formal verification, algebraic geometry |
Post-quantum signatures using AO primitives
| Name | Affiliation | Field |
|---|---|---|
| Thibauld Feneuil | CryptoExperts / Sorbonne | ZK proofs, post-quantum signatures (CAPSS) |
| Matthieu Rivain | CryptoExperts | Side-channel countermeasures, masking, white-box crypto |
| Xinyu Zhang | Monash University | Post-quantum signatures (Loquat, Pegasus) |
| Ron Steinfeld | Monash University | Lattice crypto, post-quantum crypto |
| Muhammed F. Esgin | Monash University | Post-quantum crypto |
| Joseph K. Liu | Monash University | Privacy-preserving crypto |
| Dongxi Liu | CSIRO Data61 | Applied crypto |
| Sushmita Ruj | UNSW Sydney | Blockchain, applied crypto |
| Ziyi Li | Monash University | Post-quantum signatures (Pegasus) |
| Raymond K. Zhao | Monash University | Post-quantum crypto |
| Tsz Hon Yuen | Univ. of Hong Kong | Privacy-preserving crypto |
| Jim Posen | (Vision Mark-32 co-author) | ZK proofs |
| Danilo Sijacic | prev. KU Leuven (COSIC) | Crypto hardware, side-channel analysis |
| Sundas Tariq | KU Leuven (COSIC) / 3MI Labs | AO hash design (RPO-M31, XHash-M31) |
Foundational Groebner basis / computational algebra researchers
| Name | Affiliation | Field |
|---|---|---|
| Jean-Charles Faugere | Sorbonne / Inria Paris | Groebner bases (F4, F5 algorithms), algebraic cryptanalysis |
| Daniel Lazard | Sorbonne (emeritus) | Computer algebra, Groebner bases, polynomial solving |
| Magali Bardet | Univ. Rouen Normandie | Semi-regularity complexity, algebraic cryptanalysis, code-based crypto |
| Bruno Salvy | Inria / ENS Lyon | Computer algebra, symbolic computation, asymptotics |
| Alessio Caminata | (Groebner complexity) | Solving degree, Hilbert series |
| Elisa Gorla | (Groebner complexity) | Algebraic geometry, solving degree, regularity |
| Nicolas Courtois | UCL London | Algebraic cryptanalysis (XL, XSL), block cipher analysis |
| Josef Pieprzyk | CSIRO Data61 / Macquarie Univ. | Hash functions, algebraic cryptanalysis |
| Jacques Patarin | UVSQ (Versailles) | Multivariate crypto (HFE, UOV), Feistel provable security |
| Adi Shamir | Weizmann Institute | Cryptography (RSA, differential crypto, XL). Turing Award 2002 |
| Ludovic Perret | Sorbonne / Inria / CryptoNext | Multivariate crypto, Groebner complexity, post-quantum |
| Luk Bettale | IDEMIA (prev. Sorbonne) | Hybrid polynomial solving, Groebner bases |
| Antoine Joux | CISPA Helmholtz Center | Algorithmic cryptanalysis, discrete log, pairings |
| Gregory V. Bard | Univ. Wisconsin-Stout | Algebraic cryptanalysis, SAT solvers, GF(2) linear algebra |
| Johannes Buchmann | TU Darmstadt (emeritus) | Computational number theory, lattice crypto, post-quantum |
Textbook authors (computational algebra, finite fields)
| Name | Affiliation | Field |
|---|---|---|
| David A. Cox | Amherst College (emeritus) | Algebraic geometry, toric varieties |
| John B. Little | College of the Holy Cross | Algebraic geometry, algebraic coding theory |
| Donal B. O'Shea | New College of Florida | Algebraic geometry, singularity theory |
| Martin Kreuzer | Universitat Passau | Computational commutative algebra, Groebner bases |
| Rudolf Lidl | Univ. of Tasmania (emeritus) | Finite fields, polynomials over finite fields |
| Harald Niederreiter | Austrian Academy of Sciences | Finite fields, quasi-Monte Carlo, coding theory |
| Joachim von zur Gathen | Univ. Bonn (emeritus) | Computer algebra, polynomial algorithms |
| Jurgen Gerhard | Maplesoft | Computer algebra, symbolic computation |
| Jintai Ding | XJTLU / Univ. Cincinnati (emeritus) | Multivariate crypto (MQ), post-quantum (ML-KEM) |
| Albrecht Petzoldt | (Multivariate PKC co-author) | Multivariate cryptography |
| Daniel Schmidt | (Multivariate PKC co-author) | Multivariate cryptography |
Sage implementations needed
- Poseidon reference implementation
- Poseidon2 reference implementation
- Anemoi Flystel implementation
- Groebner basis attack demo on reduced-round Poseidon
- Differential uniformity computation
- Algebraic degree growth experiments
- Interpolation attack on toy example
Content to write
- Detailed Flystel construction walkthrough
- Comparison table: constraints per hash across proof systems
- MDS matrix construction methods
- Round constant generation (Grain LFSR, etc.)
- Performance benchmarks across different fields
Open questions to investigate
- Actual vs. upper-bound algebraic degree for Poseidon partial rounds
- Semi-regularity assumption validity for each primitive
- Impact of field choice on security margins
- Relationship between constraint efficiency and security margin