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Cryptology ePrint Archive

Fast Isogeny Evaluation on Binary Curves Quick Draw Queries: Lightweight Searchable Public-key Ciphertexts with Hidden Structures via Non-Interactive Key Exchange A Constructive Treatment of Authentication Boolean Arithmetic over $\mathbb{F}_2$ from Group Commutators HAWK with Hint: Algebraic Key Recovery from Side-Channel Leakage Post-Quantum Secure k-Times Traceable Ring Signature A Key Schedule Design and Evaluation under Boundary Round-Key Leakage 2G2T: Constant-Size, Statistically Sound MSM Outsourcing Proximity Signatures Breaking Optimized HQC: The First Cache-Timing Full Decryption Oracle Key-Recovery Attack in Post-Quantum Cryptography Efficient Partially Blind Signatures from Isogenies Evaluating PQC KEMs, Combiners, and Cascade Encryption via Adaptive IND-CPA Testing Using Deep Learning High-Throughput Side-Channel-Protected Stream Cipher Hardware for 6G Systems Efficient e = 3 Threshold RSA via Integer Coordinates for Intel SGX Zeal: PIR for Non-Cooperative Databases VEIL: Lightweight Zero-Knowledge for Hash-Based Multilinear Proof Systems Witness-Indistinguishable Arguments of Knowledge and One-Way Functions The many faces of Schnorr: a touch-up Open Problems in List Decoding and Correlated Agreement Compressed Key Exchange Protocol from Orientations of Large Discriminant Using AVX-512 SPLASH: SPeculative Leakage-Adaptive Secure Hardware An Efficient Identity-Based Blind Signature Scheme from SM9 Efficient Batch Threshold Encryption Using Partial Fraction Techniques A note on the Unsuitability of LIGA for Linkable Ring Signatures: The perils of non-commutativity Verification Facade: Masquerading Insecure Cryptographic Implementations as Verified Code Cryptographic Implications of Worst-Case Hardness of Time-Bounded Kolmogorov Complexity Efficient Merkle-Tree Consistent Accumulator FLOSS: Fast Linear Online Secret-Shared Shuffling Which Privacy Blanket is Optimal in the Shuffle Model? Applications of Bruhat-Chevalley-Renner Decomposition to Metric-Aware Code-Based Cryptography
Short Pairing-based Non-interactive Zero-Knowledge Arguments
Jens Groth · 2009-08-15 · via Cryptology ePrint Archive

Paper 2009/390

Short Pairing-based Non-interactive Zero-Knowledge Arguments

Abstract

We construct non-interactive zero-knowledge arguments for circuit satisfiability with perfect completeness, perfect zero knowledge and computational soundness. The non-interactive zero-knowledge arguments have sublinear size and very efficient public verification. Their size can even be reduced to a constant number of group elements if we allow the common reference string to be large. Our constructions rely on groups with pairings, and security is based on two new cryptographic assumptions; we do not use the Fiat-Shamir heuristic or random oracles.

Note: First pairing-based zk-SNARK, first non-Fiat-Shamir SNARK, published at ASIACRYPT 2010 This revision: polished and fixed typos, added context on relation to later zk-SNARKs Lipmaa12, GGPR13 and on universal and updatable CRS from GKMMM18, addendum on preprocessing for fixed circuit

BibTeX 

@misc{cryptoeprint:2009/390,
      author = {Jens Groth},
      title = {Short Pairing-based Non-interactive Zero-Knowledge Arguments},
      howpublished = {Cryptology {ePrint} Archive, Paper 2009/390},
      year = {2009},
      url = {https://eprint.iacr.org/2009/390}
}

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