Efficient Noninteractive Proof Systems for Bilinear Groups

By Jens Groth, Amit Sahai. 2008

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Bulletproofs: Short Proofs for Confidential Transactions and More (2018, background): “Many efficient non-interactive zero-knowledge proofs and arguments for arithmetic circuit satisfiability have been developed [4]–[6], [32]–[34], and highly efficient protocols are known.”
Geppetto: Versatile Verifiable Computation (2015, methodology): “Escala and Groth [26] design CP schemes from Groth-Sahai proofs [34].”
Faster Explicit Formulas for Computing Pairings over Ordinary Curves (2011, background): “The performance of pairing computation has received increasing interest in the research community, mainly because Pairing-Based Cryptography enables efficient and elegant solutions to several longstanding problems in cryptography such as Identity-Based Encryption [1,2], powerful non-interactive zero”
Short Pairing-Based Non-interactive Zero-Knowledge Arguments (2010, background): “In some special cases, for instance in the ring signature of Chandran, Groth and Sahai [CGS07], these techniques lead to sub-linear size NIZK proofs but in general the number of group elements in an NIZK proof grows linearly in the size of the statement.”
Decentralizing Attribute-Based Encryption (2011, methodology): “We note that several systems such as BGN encryption [15], GrothOstrovsky-Sahai NIZK proofs [32], traitor tracing [16] , and predicate encryption [17, 36] were originally developed in the composite order setting, but later variants were developed in prime order groups [31, 48, 33, 35, 25, 26, 37].”
Quadratic Span Programs and Succinct NIZKs without PCPs (2013, background): “[28, 29] previously constructed NIZKs over bilinear groups with various attractive properties, but with size linear in the circuit.”
An Algebraic Framework for Diffie–Hellman Assumptions (2013, methodology): “It has found applications to encryption [23], signatures [2], zero-knowledge proofs [17], pseudorandom functions [4] and many more.”
Automated Synthesis of Privacy-Preserving Distributed Applications (2011, methodology): “The validity of this predicate is ruled by the authorization policy (1) and the minimal amount of information the student has to reveal is captured by formula (2).”
Attribute-Based Signatures (2011, methodology): “We refer the reader to [22] for detailed definitions of non-interactive witness-indistinguishable (NIWI) proofs, but give a brief overview of the necessary definitions here.”
Post-Quantum Zero-Knowledge and Signatures from Symmetric-Key Primitives (2017, background): “, discrete logarithms [28, 80] or equations over bilinear groups [51].”
New Software Speed Records for Cryptographic Pairings (2010, background): “Still, new protocols including the computation of a large number of pairings or pairing products [13, 21] demand even faster pairings.”
Hierarchical Predicate Encryption for Inner-Products (2009, methodology): “Higher dimensional vector treatment of bilinear pairing groups have been already employed in the literature especially in the areas of IBE, ABE and BE (e.g., [4,1,6,8,13,14,21]).”
Scalable, transparent, and post-quantum secure computational integrity (2018, background): “al [53] (see [64, 52, 81, 30, 62, 63] for related work and further improvements).”
A Survey of Verifiable Computation (2017, methodology): “Backes et al. designed a compiler [73] based on Groth-Sahai ZK proofs [74] and used it to handle logical formulas.”
Succinct Malleable NIZKs and an Application to Compact Shuffles (2013, methodology): “Specifically, their approach builds heavily on the Groth-Sahai proof system [24]; this means that they can consider only relations on group elements in groups that admit bilinear pairings, and it might therefore seem as though controlled malleability were just a property of the Groth-Sahai proof sys”
Converting Pairing-Based Cryptosystems from Composite-Order Groups to Prime-Order Groups (2010, background): “, [1, 20]) have called the assumption that DDH is infeasible in both G1 and G2 the symmetric external Diffie-Hellman assumption, or SXDH.”