Multi-bit Cryptosystems Based on Lattice Problems

By Akinori Kawachi, Keisuke Tanaka, Keita Xagawa. 2006

100 citations recorded by the source corpus.

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In Artificial Intelligence

Citations in the corpus

A Review of Homomorphic Encryption Libraries for Secure Computation (2018, background): “Partially Homomorphic Encryption (PHE) schemes such as [9,10,11,12,13,14,15,16,17,18,19] allow only one type of operation any number of times - either addition or multiplication on encrypted data as compared to Somewhat Homomorphic schemes that support both.”
A Survey on Homomorphic Encryption Schemes (2017, methodology): “There are several useful PHE examples [Rivest et al. 1978b; Goldwasser and Mi-cali 1982; ElGamal 1985; Benaloh 1994; Naccache and Stern 1998; Okamoto and Uchiyama 1998; Paillier 1999; Damgård and Jurik 2001; Kawachi et al. 2007] in the literature.”
A Comprehensive Survey of Privacy-preserving Federated Learning (2021, background): “Partially homomorphic encryption only supports either additive or multiplicative operations, which are referred to as additively homomorphic encryption [88] and multiplicative homomorphic encryption [46], respectively.”
Frodo: Take off the Ring! Practical, Quantum-Secure Key Exchange from LWE (2016, background): “Constructions based on LWE have led to a large variety of public-key cryptosystems [38, 52, 31, 18, 3, 2, 17].”
Lattice-Based Cryptography (2006, unknown): “[32].”
On lattices, learning with errors, random linear codes, and cryptography (2005, background): “First, Kawachi, Tanaka, and Xagawa [21] proposed a modification to our cryptosystem that slightly improves the encryption blowup to O(n), essentially getting rid of a log factor.”
Lossy trapdoor functions and their applications (2008, methodology): “This basic cryptosystem is similar to Regev’s public key cryptosystem [34] and its multi-bit variant [27].”
Fully homomorphic encryption using ideal lattices (2009, background): “Some additively homomorphic encryption schemes use lattices or linear codes [22, 50, 27 , 36, 37, 4]. ElGamal [20] is multiplicatively homomorphic.”
Public-key cryptosystems from the worst-case shortest vector problem: extended abstract (2009, background): “(As observed in [18, 25], it is even possible to reduce the expansion to O(1) by fitting Ω(log q′) bits into each component of g2, at the expense of a somewhat smaller α.”
Privacy‐preserving federated learning based on multi‐key homomorphic encryption (2021, methodology): “Popular additive homomorphic encryption (HE) schemes include Goldwasser and Micali [9], Paillier [10], Damgard and Jurik [11], or Kawachi et al. [12].”
On lattices, learning with errors, random linear codes, and cryptography (2009, background): “First, Kawachi, Tanaka, and Xagawa [21] proposed a modification to our cryptosystem that slightly improves the encryption blowup to O(n), essentially getting rid of a log factor.”
Trapdoors for hard lattices and new cryptographic constructions (2008, background): “As shown in [ KTX07 , PVW07], message bits can also be replaced with elements of Zp, where p = nc 0, at the expense of a smaller noise parameter (and thus a”