On Diophantine Complexity and Statistical Zero-Knowledge Arguments

By Helger Lipmaa. 2003

179 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Statistics and Probability

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Citations in the corpus

Bulletproofs: Short Proofs for Confidential Transactions and More (2018, background): “Lipmaa [Lip03] presents a range proof which uses integer commitments, and Lagrange’s four-square theorem which states that every positive integer y can be expressed as a sum of four squares.”
Additive Combinatorics and Discrete Logarithm Based Range Protocols (2010, background): “As discussed in the introduction, some efficient range proofs were proposed in [4, 16, 15, 5].”
Non-interactive Zero-Knowledge Arguments for Voting (2005, methodology): “Having received many such encrypted votes we may by the homomorphic property of the cryptosystem multiply all the ciphertexts and get a new ciphertext C = 3 As an alternative Lipmaa [Lip03] has suggested to encode votes as Lucas numbers.”
Optimal Rate Private Information Retrieval from Homomorphic Encryption (2015, background): “(This approach works when w = 2, in the case w > 2 one can use efficient range proofs [4, 6, 24].”
A Certifying Compiler for Zero-Knowledge Proofs of Knowledge Based on Sigma-Protocols (2010, background): “Examples of protocols that can be automatically generated by our compiler include [3,4,5,6,7,8,9,10,13,14,15,16].”
Transparent SNARKs from DARK Compilers (2020, methodology): “Lipmaa drew the link between zero-knowledge proofs constructed from integer commitment schemes and Diophantine complexity [42], coining the term Diophantine Arguments of Knowledge .”
Efficient, Robust and Constant-Round Distributed RSA Key Generation (2010, background): “Any positive number can be written as the sum of four squares which efficiently can be calculated [17].”
Efficient RSA Key Generation and Threshold Paillier in the Two-Party Setting (2012, background): “An alternative solution is to take a detour around integer commitments; this allows a solution requiring only O(1) exponentiations [7,24,49].”
Efficient Protocols for Set Membership and Range Proofs (2008, methodology): “2 Lipmaa’s range proof Lipmaa followed the positivity property of square numbers and proposed to prove positivity by decomposing the secret number into the sum of four square (see [13] and [14]).”