A New Public-Key Cryptosystem as Secure as Factoring

By Tatsuaki Okamoto, S. Uchiyama. 1998

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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.”
Le chiffrement asymétrique et la sécurité prouvée (2002, background): “Cela provient en fait de leur résistance face aux multiples attaques qui ont été mises en œuvre depuis plus de 20 ans [16,17].”
Efficient Proofs that a Committed Number Lies in an Interval (2000, methodology): “Charlie and Deborah use the Okamoto-Uchiyama [18] rC C mod n C , where r C is randomly selected over Z * nC .”
Non-interactive cryptocomputing for NC/sup 1/ (1999, background): “Recently, [ 31 , 33] introduced homomorphic encryption schemes over different groups.”
Privacy-preserving SVM classification (2008, unknown): “There are several homorphic encryption systems such as the Goldwasser–Micali cryptosystem [5], the Benaloh cryptosystem [4], the Naccache–Stern cryptosystem[25], the Paillier cryptosystem [28], and the Okamoto–Uchiyama cryptosystem [26], any of which can be used in practice.”
Structure-Preserving Signatures and Commitments to Group Elements (2010, background): “Homomorphic cryptosystems such as [ElG86, OU98 , Pai99, BGN05] or Linear Encryption [BBS04] can be seen as homomorphic commitment schemes that are perfectly binding and computationally hiding.”
A Certifying Compiler for Zero-Knowledge Proofs of Knowledge Based on Sigma-Protocols (2010, unknown): “For instance, it can be used to prove knowledge of the content of ciphertexts under the Cramer/Shoup [50] or the RSA [51] encryption schemes, and many others [52,53,54,55,56].”
Public-Key Cryptosystems Based on Composite Degree Residuosity Classes (1999, background): “Later, Naccache and Stern [16], and independently Okamoto and Uchiyama [19] significantly extended the encryption rate by investigating two different approaches: residuosity of smooth degree in Zpq and residuosity of prime degree p in Z ∗ pq respectively.”
Privacy-preserving Naïve Bayes classification (2008, methodology): “The key idea behind the protocol is to use a homomorphic encryption system such as the Goldwasser– Micali cryptosystem [4], the Benaloh cryptosystem [3], the Naccache–Stern cryptosystem [30], the Paillier cryptosystem [34], and the Okamoto–Uchiyama cryptosystem [33].”
Modern Cryptography: Theory and Practice (2003, background): “The reader is referred to [229, 224, 228] for the technical details.”
A new public key cryptosystem based on higher residues (1998, result): “After the completion of the present work, we have been informed that another homomorphic probabilistic encryption scheme, using moduli n of the form p2q, where p and q are primes, had been found by Okamoto and Uchiyama (see [22]), achieving an expansion rate similar to ours.”
Semi-Homomorphic Encryption and Multiparty Computation (2011, methodology): “These include: the Okamoto-Uchiyama cryptosystem [ OU98 ]; Paillier cryptosystem [Pai99] and its generalization by Damg˚ ard and Jurik [DJ01]; Regev’s LWE based cryptosystem [Reg05]; the scheme of Damg˚ ard, Geisler and Kroigaard [DGK09] based on a subgroup-decision problem; the subset-sum based sch”
Practical multi-candidate election system (2001, methodology): “A solution is to use a trapdoor discrete logarithm scheme with large band- width such as Naccache-Stern [22], Okamoto-Uchiyama [26], or Paillier [27].”
Privacy Preserving Deep Computation Model on Cloud for Big Data Feature Learning (2016, methodology): “For example, some representative additively homomorphic encryption schemes are Okamoto-Uchiyama [40], Pallier [41] and Damard-Jurik [42] while RSA [37] and ElGamal [43] are representatives of the multiplicatively homomorphic encryption schemes.”
Sharing Decryption in the Context of Voting or Lotteries (2000, background): “Most homomorphic cryptosystems as Goldwasser-Micali's 11], Benaloh's 1, 4], Naccache-Stern's 12], Okamoto-Uchiyama's 13] or Paillier's 14] cryptosystems need to distribute a secret value related to the factorization of an RSA modulus.”
Evaluating 2-DNF Formulas on Ciphertexts (2005, methodology): “The system resembles the Paillier [28] and the Okamoto-Uchiyama [27] encryption schemes.”