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TomWambsgans May 16, 2026
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proof logup
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zerocheck
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batched zerocheck
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\subsubsection{Attaching evaluation claims}\label{sec:air-eval}
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Beyond consecutive sampling of the challenge
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instruction encoding
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execution AIR
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Avoid paying for (most of) the zero suffix from polynomial stacking
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\subsection{Small-Value Optimization (SVO) and Split-Eq}\label{sec:svo}
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AIR constraints
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bus
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logup GKR
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\subsection{End-to-end protocol}
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\subsection{Fiat-Shamir}
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naming
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\subsection{Functions}
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corrections
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317 changes: 209 additions & 108 deletions misc/bibliography.bib
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@article{whir,
author = {Gal Arnon and Alessandro Chiesa and Giacomo Fenzi and Eylon Yogev},
title = {{WHIR}: Reed–Solomon Proximity Testing with Super-Fast Verification},
howpublished = {Cryptology {ePrint} Archive, Paper 2024/1586},
year = {2024},
url = {https://eprint.iacr.org/2024/1586}
author = {Gal Arnon and Alessandro Chiesa and Giacomo Fenzi and Eylon Yogev},
title = {{WHIR}: Reed–Solomon Proximity Testing with Super-Fast Verification},
howpublished = {Cryptology {ePrint} Archive, Paper 2024/1586},
year = {2024},
url = {https://eprint.iacr.org/2024/1586}
}
@article{fri_binius,
author = {Benjamin E. Diamond and Jim Posen},
title = {Polylogarithmic Proofs for Multilinears over Binary Towers},
howpublished = {Cryptology {ePrint} Archive, Paper 2024/504},
year = {2024},
url = {https://eprint.iacr.org/2024/504}
author = {Benjamin E. Diamond and Jim Posen},
title = {Polylogarithmic Proofs for Multilinears over Binary Towers},
howpublished = {Cryptology {ePrint} Archive, Paper 2024/504},
year = {2024},
url = {https://eprint.iacr.org/2024/504}
}
@article{ccs,
author = {Srinath Setty and Justin Thaler and Riad Wahby},
title = {Customizable constraint systems for succinct arguments},
howpublished = {Cryptology {ePrint} Archive, Paper 2023/552},
year = {2023},
url = {https://eprint.iacr.org/2023/552}
author = {Srinath Setty and Justin Thaler and Riad Wahby},
title = {Customizable constraint systems for succinct arguments},
howpublished = {Cryptology {ePrint} Archive, Paper 2023/552},
year = {2023},
url = {https://eprint.iacr.org/2023/552}
}
@article{simple_multivariate_AIR,
author = {William Borgeaud},
title = {A simple multivariate AIR argument inspired by SuperSpartan},
year = {2023},
url = {https://solvable.group/posts/super-air/}
author = {William Borgeaud},
title = {A simple multivariate AIR argument inspired by SuperSpartan},
year = {2023},
url = {https://solvable.group/posts/super-air/}
}
@article{hyperplonk,
author = {Binyi Chen and Benedikt Bünz and Dan Boneh and Zhenfei Zhang},
title = {{HyperPlonk}: Plonk with Linear-Time Prover and High-Degree Custom Gates},
howpublished = {Cryptology {ePrint} Archive, Paper 2022/1355},
year = {2022},
url = {https://eprint.iacr.org/2022/1355}
author = {Binyi Chen and Benedikt Bünz and Dan Boneh and Zhenfei Zhang},
title = {{HyperPlonk}: Plonk with Linear-Time Prover and High-Degree Custom Gates},
howpublished = {Cryptology {ePrint} Archive, Paper 2022/1355},
year = {2022},
url = {https://eprint.iacr.org/2022/1355}
}
@article{univariate_skip,
author = {Angus Gruen},
title = {Some Improvements for the {PIOP} for {ZeroCheck}},
howpublished = {Cryptology {ePrint} Archive, Paper 2024/108},
year = {2024},
url = {https://eprint.iacr.org/2024/108}
author = {Angus Gruen},
title = {Some Improvements for the {PIOP} for {ZeroCheck}},
howpublished = {Cryptology {ePrint} Archive, Paper 2024/108},
year = {2024},
url = {https://eprint.iacr.org/2024/108}
}
@misc{eth_stark,
author = {StarkWare},
title = {{ethSTARK} Documentation},
howpublished = {Cryptology {ePrint} Archive, Paper 2021/582},
year = {2021},
url = {https://eprint.iacr.org/2021/582}
author = {StarkWare},
title = {{ethSTARK} Documentation},
howpublished = {Cryptology {ePrint} Archive, Paper 2021/582},
year = {2021},
url = {https://eprint.iacr.org/2021/582}
}


@misc{ethereum_signatures,
author = {Justin Drake and Dmitry Khovratovich and Mikhail Kudinov and Benedikt Wagner},
title = {Hash-Based Multi-Signatures for Post-Quantum Ethereum},
howpublished = {Cryptology {ePrint} Archive, Paper 2025/055},
year = {2025},
doi = {10.62056/aey7qjp10},
url = {https://eprint.iacr.org/2025/055}
author = {Justin Drake and Dmitry Khovratovich and Mikhail Kudinov and Benedikt Wagner},
title = {Hash-Based Multi-Signatures for Post-Quantum Ethereum},
howpublished = {Cryptology {ePrint} Archive, Paper 2025/055},
year = {2025},
doi = {10.62056/aey7qjp10},
url = {https://eprint.iacr.org/2025/055}
}

@misc{proximity_gaps_rs_codes,
author = {Eli Ben-Sasson and Dan Carmon and Yuval Ishai and Swastik Kopparty and Shubhangi Saraf},
title = {Proximity Gaps for Reed-Solomon Codes},
howpublished = {Cryptology {ePrint} Archive, Paper 2020/654},
year = {2020},
url = {https://eprint.iacr.org/2020/654}
author = {Eli Ben-Sasson and Dan Carmon and Yuval Ishai and Swastik Kopparty and Shubhangi Saraf},
title = {Proximity Gaps for Reed-Solomon Codes},
howpublished = {Cryptology {ePrint} Archive, Paper 2020/654},
year = {2020},
url = {https://eprint.iacr.org/2020/654}
}

@misc{cairo,
author = {Lior Goldberg and Shahar Papini and Michael Riabzev},
title = {Cairo – a Turing-complete {STARK}-friendly {CPU} architecture},
howpublished = {Cryptology {ePrint} Archive, Paper 2021/1063},
year = {2021},
url = {https://eprint.iacr.org/2021/1063}
author = {Lior Goldberg and Shahar Papini and Michael Riabzev},
title = {Cairo – a Turing-complete {STARK}-friendly {CPU} architecture},
howpublished = {Cryptology {ePrint} Archive, Paper 2021/1063},
year = {2021},
url = {https://eprint.iacr.org/2021/1063}
}

@misc{spice,
author = {Srinath Setty and Sebastian Angel and Trinabh Gupta and Jonathan Lee},
title = {Proving the correct execution of concurrent services in zero-knowledge},
howpublished = {Cryptology {ePrint} Archive, Paper 2018/907},
year = {2018},
url = {https://eprint.iacr.org/2018/907}
author = {Srinath Setty and Sebastian Angel and Trinabh Gupta and Jonathan Lee},
title = {Proving the correct execution of concurrent services in zero-knowledge},
howpublished = {Cryptology {ePrint} Archive, Paper 2018/907},
year = {2018},
url = {https://eprint.iacr.org/2018/907}
}
@misc{top_hypercube,
author = {Dmitry Khovratovich and Mikhail Kudinov and Benedikt Wagner},
title = {At the Top of the Hypercube -- Better Size-Time Tradeoffs for Hash-Based Signatures},
howpublished = {Cryptology {ePrint} Archive, Paper 2025/889},
year = {2025},
url = {https://eprint.iacr.org/2025/889}
author = {Dmitry Khovratovich and Mikhail Kudinov and Benedikt Wagner},
title = {At the Top of the Hypercube -- Better Size-Time Tradeoffs for Hash-Based Signatures},
howpublished = {Cryptology {ePrint} Archive, Paper 2025/889},
year = {2025},
url = {https://eprint.iacr.org/2025/889}
}

@misc{poseidon1,
author = {Lorenzo Grassi and Dmitry Khovratovich and Christian Rechberger and Arnab Roy and Markus Schofnegger},
title = {Poseidon: A New Hash Function for Zero-Knowledge Proof Systems},
howpublished = {Cryptology {ePrint} Archive, Paper 2019/458},
year = {2019},
url = {https://eprint.iacr.org/2019/458}
author = {Lorenzo Grassi and Dmitry Khovratovich and Christian Rechberger and Arnab Roy and Markus Schofnegger},
title = {Poseidon: A New Hash Function for Zero-Knowledge Proof Systems},
howpublished = {Cryptology {ePrint} Archive, Paper 2019/458},
year = {2019},
url = {https://eprint.iacr.org/2019/458}
}


@misc{poseidon2,
author = {Lorenzo Grassi and Dmitry Khovratovich and Markus Schofnegger},
title = {Poseidon2: A Faster Version of the Poseidon Hash Function},
howpublished = {Cryptology {ePrint} Archive, Paper 2023/323},
year = {2023},
url = {https://eprint.iacr.org/2023/323}
author = {Lorenzo Grassi and Dmitry Khovratovich and Markus Schofnegger},
title = {Poseidon2: A Faster Version of the Poseidon Hash Function},
howpublished = {Cryptology {ePrint} Archive, Paper 2023/323},
year = {2023},
url = {https://eprint.iacr.org/2023/323}
}

@misc{logup_star,
author = {Lev Soukhanov},
title = {Logup*: faster, cheaper logup argument for small-table indexed lookups},
howpublished = {Cryptology {ePrint} Archive, Paper 2025/946},
year = {2025},
url = {https://eprint.iacr.org/2025/946}
author = {Lev Soukhanov},
title = {Logup*: faster, cheaper logup argument for small-table indexed lookups},
howpublished = {Cryptology {ePrint} Archive, Paper 2025/946},
year = {2025},
url = {https://eprint.iacr.org/2025/946}
}

@misc{LeanSig,
author = {Justin Drake and Dmitry Khovratovich and Mikhail Kudinov and Benedikt Wagner},
title = {Technical Note: {LeanSig} for Post-Quantum Ethereum},
howpublished = {Cryptology {ePrint} Archive, Paper 2025/1332},
year = {2025},
url = {https://eprint.iacr.org/2025/1332}
author = {Justin Drake and Dmitry Khovratovich and Mikhail Kudinov and Benedikt Wagner},
title = {Technical Note: {LeanSig} for Post-Quantum Ethereum},
howpublished = {Cryptology {ePrint} Archive, Paper 2025/1332},
year = {2025},
url = {https://eprint.iacr.org/2025/1332}
}

@misc{jagged_pcs,
author = {Tamir Hemo and Kevin Jue and Eugene Rabinovich and Gyumin Roh and Ron D. Rothblum},
title = {Jagged Polynomial Commitments (or: How to Stack Multilinears)},
howpublished = {Cryptology {ePrint} Archive, Paper 2025/917},
year = {2025},
url = {https://eprint.iacr.org/2025/917}
author = {Tamir Hemo and Kevin Jue and Eugene Rabinovich and Gyumin Roh and Ron D. Rothblum},
title = {Jagged Polynomial Commitments (or: How to Stack Multilinears)},
howpublished = {Cryptology {ePrint} Archive, Paper 2025/917},
year = {2025},
url = {https://eprint.iacr.org/2025/917}
}

@misc{proximity_gaps_rs_codes_2,
author = {Eli Ben-Sasson and Dan Carmon and Ulrich Haböck and Swastik Kopparty and Shubhangi Saraf},
title = {On Proximity Gaps for Reed–Solomon Codes},
howpublished = {Cryptology {ePrint} Archive, Paper 2025/2055},
year = {2025},
url = {https://eprint.iacr.org/2025/2055}
author = {Eli Ben-Sasson and Dan Carmon and Ulrich Haböck and Swastik Kopparty and Shubhangi Saraf},
title = {On Proximity Gaps for Reed–Solomon Codes},
howpublished = {Cryptology {ePrint} Archive, Paper 2025/2055},
year = {2025},
url = {https://eprint.iacr.org/2025/2055}
}

@misc{logup,
author = {Ulrich Haböck},
title = {Multivariate lookups based on logarithmic derivatives},
howpublished = {Cryptology {ePrint} Archive, Paper 2022/1530},
year = {2022},
url = {https://eprint.iacr.org/2022/1530}
author = {Ulrich Haböck},
title = {Multivariate lookups based on logarithmic derivatives},
howpublished = {Cryptology {ePrint} Archive, Paper 2022/1530},
year = {2022},
url = {https://eprint.iacr.org/2022/1530}
}

@misc{logup_gkr,
author = {Shahar Papini and Ulrich Haböck},
title = {Improving logarithmic derivative lookups using {GKR}},
howpublished = {Cryptology {ePrint} Archive, Paper 2023/1284},
year = {2023},
url = {https://eprint.iacr.org/2023/1284}
author = {Shahar Papini and Ulrich Haböck},
title = {Improving logarithmic derivative lookups using {GKR}},
howpublished = {Cryptology {ePrint} Archive, Paper 2023/1284},
year = {2023},
url = {https://eprint.iacr.org/2023/1284}
}

@misc{openvm,
author = {OPENVM CONTRIBUTORS},
title = {OPENVM WHITEPAPER},
year = {2025},
url = {https://openvm.dev/whitepaper.pdf}
author = {OPENVM CONTRIBUTORS},
title = {OPENVM WHITEPAPER},
year = {2025},
url = {https://openvm.dev/whitepaper.pdf}
}

@misc{sponge_indifferentiable,
author = {Gorjan Alagic and Joseph Carolan and Christian Majenz and Saliha Tokat},
title = {The Sponge is Quantum Indifferentiable},
howpublished = {Cryptology {ePrint} Archive, Paper 2025/731},
author = {Gorjan Alagic and Joseph Carolan and Christian Majenz and Saliha Tokat},
title = {The Sponge is Quantum Indifferentiable},
howpublished = {Cryptology {ePrint} Archive, Paper 2025/731},
year = {2025},
url = {https://eprint.iacr.org/2025/731}
}

@inproceedings{bls,
author = {Boneh, Dan
and Lynn, Ben
and Shacham, Hovav},
editor = {Boyd, Colin},
title = {Short Signatures from the Weil Pairing},
booktitle = {Advances in Cryptology --- ASIACRYPT 2001},
year = {2001},
publisher = {Springer Berlin Heidelberg},
address = {Berlin, Heidelberg},
pages = {514--532},
abstract = {We introduce a short signature scheme based on the Computational Diffie-Hellman assumption on certain elliptic and hyper-elliptic curves. The signature length is half the size of a DSA signature for a similar level of security. Our short signature scheme is designed for systems where signatures are typed in by a human or signatures are sent over a low-bandwidth channel.},
isbn = {978-3-540-45682-7}
}

@article{ecdsa,
title = {The Elliptic Curve Digital Signature Algorithm (ECDSA)},
author = {Donald Byron Johnson and Alfred Menezes and Scott A. Vanstone},
journal = {International Journal of Information Security},
year = {2001},
volume = {1},
pages = {36-63},
url = {https://api.semanticscholar.org/CorpusID:207063673}
}

@inproceedings{kzg,
author = {Kate, Aniket
and Zaverucha, Gregory M.
and Goldberg, Ian},
editor = {Abe, Masayuki},
title = {Constant-Size Commitments to Polynomials and Their Applications},
booktitle = {Advances in Cryptology - ASIACRYPT 2010},
year = {2010},
publisher = {Springer Berlin Heidelberg},
address = {Berlin, Heidelberg},
pages = {177--194},
abstract = {We introduce and formally define polynomial commitment schemes, and provide two efficient constructions. A polynomial commitment scheme allows a committer to commit to a polynomial with a short string that can be used by a verifier to confirm claimed evaluations of the committed polynomial. Although the homomorphic commitment schemes in the literature can be used to achieve this goal, the sizes of their commitments are linear in the degree of the committed polynomial. On the other hand, polynomial commitments in our schemes are of constant size (single elements). The overhead of opening a commitment is also constant; even opening multiple evaluations requires only a constant amount of communication overhead. Therefore, our schemes are useful tools to reduce the communication cost in cryptographic protocols. On that front, we apply our polynomial commitment schemes to four problems in cryptography: verifiable secret sharing, zero-knowledge sets, credentials and content extraction signatures.},
isbn = {978-3-642-17373-8}
}

@article{shor,
title = {Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer},
volume = {26},
issn = {1095-7111},
url = {http://dx.doi.org/10.1137/S0097539795293172},
doi = {10.1137/s0097539795293172},
number = {5},
journal = {SIAM Journal on Computing},
publisher = {Society for Industrial & Applied Mathematics (SIAM)},
author = {Shor, Peter W.},
year = {1997},
month = Oct,
pages = {1484–1509}
}

@article{sumcheck,
author = {Lund, Carsten and Fortnow, Lance and Karloff, Howard and Nisan, Noam},
year = {1999},
month = {04},
pages = {},
title = {Algebraic Methods for Interactive Proof Systems},
volume = {39},
journal = {Journal of the ACM},
doi = {10.1145/146585.146605}
}

@misc{sphincs_plus,
author = {Daniel J. Bernstein and Andreas Hülsing and Stefan Kölbl and Ruben Niederhagen and Joost Rijneveld and Peter Schwabe},
title = {The {SPHINCS}+ Signature Framework},
howpublished = {Cryptology {ePrint} Archive, Paper 2019/1086},
year = {2019},
doi = {10.1145/3319535.3363229},
url = {https://eprint.iacr.org/2019/1086}
}

@misc{Speeding-Up-Sum-Check-Proving,
author = {Suyash Bagad and Quang Dao and Yuval Domb and Justin Thaler},
title = {Speeding Up Sum-Check Proving},
howpublished = {Cryptology {ePrint} Archive, Paper 2025/1117},
year = {2025},
url = {https://eprint.iacr.org/2025/1117}
}

@misc{fiat_shamir_duplex_sponge,
author = {Alessandro Chiesa and Michele Orrù},
title = {A Fiat–Shamir Transformation From Duplex Sponges},
howpublished = {Cryptology {ePrint} Archive, Paper 2025/536},
year = {2025},
url = {https://eprint.iacr.org/2025/731}
doi = {10.1007/978-3-032-12287-2_16},
url = {https://eprint.iacr.org/2025/536}
}

@misc{BCS,
author = {Eli Ben-Sasson and Alessandro Chiesa and Nicholas Spooner},
title = {Interactive Oracle Proofs},
howpublished = {Cryptology {ePrint} Archive, Paper 2016/116},
year = {2016},
url = {https://eprint.iacr.org/2016/116}
}

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