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Commitments with Efficient Zero-Knowledge Arguments from Subset Sum Problems

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Computer Security – ESORICS 2023 (ESORICS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14344))

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Abstract

We present a cryptographic string commitment scheme that is computationally hiding and binding based on (modular) subset sum problems. It is believed that these NP-complete problems provide post-quantum security contrary to the number theory assumptions currently used in cryptography. Using techniques recently introduced by Feneuil, Maire, Rivain and Vergnaud, this simple commitment scheme enables an efficient zero-knowledge proof of knowledge for committed values as well as proofs showing Boolean relations amongst the committed bits. In particular, one can prove that committed bits \(m_0, m_1, ..., m_\ell \) satisfy \(m_0 = C(m_1, ..., m_\ell )\) for any Boolean circuit C (without revealing any information on those bits). The proof system achieves good communication and computational complexity since for a security parameter \(\lambda \), the protocol’s communication complexity is \(\tilde{O}(|C| \lambda + \lambda ^2)\) (compared to \(\tilde{O}(|C| \lambda ^2)\) for the best code-based protocol due to Jain, Krenn, Pietrzak and Tentes).

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Authors and Affiliations

  1. Sorbonne Université, CNRS, LIP6, 75005, Paris, France

    Jules Maire & Damien Vergnaud

Authors
  1. Jules Maire
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  2. Damien Vergnaud
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Corresponding author

Correspondence to Jules Maire .

Editor information

Editors and Affiliations

  1. University of California, Irvine, CA, USA

    Gene Tsudik

  2. University of Padua, Padua, Italy

    Mauro Conti

  3. Delft University of Technology, Delft, The Netherlands

    Kaitai Liang

  4. Delft University of Technology, Delft, The Netherlands

    Georgios Smaragdakis

A Description of Protocols 3 and 4

A Description of Protocols 3 and 4

In order to describe the circuit during Protocol 3, we set \(S \leftarrow \emptyset \). Then construct S as follows: if \(m_{x_k}^\ell \wedge m_{y_k}^{\ell _k}=m_{z_k}^{\ell '_k}\) for \(k \in [1,M], \{\ell ,\ell _k,\ell _k'\} \in [1,L]^3, \{x_k,y_k,z_k\} \in [1,n]^3\), then \(S=S\cup \{(\ell ,x_k;\ell _k,y_k;\ell '_k,z_k)\}\).

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Maire, J., Vergnaud, D. (2024). Commitments with Efficient Zero-Knowledge Arguments from Subset Sum Problems. In: Tsudik, G., Conti, M., Liang, K., Smaragdakis, G. (eds) Computer Security – ESORICS 2023. ESORICS 2023. Lecture Notes in Computer Science, vol 14344. Springer, Cham. https://doi.org/10.1007/978-3-031-50594-2_10

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  • DOI: https://doi.org/10.1007/978-3-031-50594-2_10

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  • Online ISBN: 978-3-031-50594-2

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