全同态加密技术文章分类

原文地址：http://xagawa.net/bib-lattice/?FHEs

Fully HomomorphicOnes †

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Before Gentry'sFHE †

• [BGN]
• [GHV10-EC] Craig Gentry, Shai Halevi, Vinod Vaikuntanathan: ASimple BGN-Type Cryptosystem from LWE. EUROCRYPT 2010

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PreLWE †

• [Gen09-STOC] C. Gentry. “Fully homomorphic encryption usingideal lattices.” (STOC 2009)
  • Based on ideal lattices. KDM-CPA security serves fullyhomomorphic encryption by simulating the decryption circuit. Thedescriptions and several proofs appeared in [Gen09-Thesis].
• [SV10-PKC] N. P. Smart and F. Vercauteren. “Fully HomomorphicEncryption with Relatively Small Key and Ciphertext Sizes.” (PKC2010,http://eprint.iacr.org/2009/571 )
  • The ciphertext is an element in Z_p by basing the special ideallattice.
• [Gen10-C] Craig Gentry: Toward Basing Fully HomomorphicEncryption on Worst-Case Hardness. CRYPTO 2010
  • See also his thesis.
• [SS10-AC] D. Stehlé and R. Steinfeld. “Faster Fully HomomorphicEncryption.” (ASIACRYPT 2010, http://eprint.iacr.org/2010/299 )

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From(Ring)LWE †

• [BV11-C] Zvika Brakerski, Vinod Vaikuntanathan: FullyHomomorphic Encryption from Ring-LWE and Security for Key DependentMessages. CRYPTO 2011
• [BV11-FOCS] Zvika Brakerski, Vinod Vaikuntanathan: EfficientFully Homomorphic Encryption from (Standard) LWE. FOCS 2011
• [BGV12-ITCS] Zvika Brakerski, Craig Gentry, VinodVaikuntanathan: (Leveled) fully homomorphic encryption withoutbootstrapping. ITCS 2012
• [Bra12-C] Zvika Brakerski: Fully Homomorphic Encryption withoutModulus Switching from Classical GapSVP. (CRYPTO 2012, ePrint2012/078)
• [FV12] Junfeng Fan and Frederik Vercauteren: Somewhat PracticalFully Homomorphic Encryption. http://eprint.iacr.org/2012/144
  • Porting the scheme in [Bra12-C] to Ring-LWE setting.
• [GHPS12-SCN]] Craig Gentry, Shai Halevi, Chris Peikert, andNigel P. Smart. “Ring Switching in BGV-Style HomomorphicEncryption.” (SCN 2012)

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From approximate GCDand its variants †

• [vDGHV10-EC] M. van Dijk, C. Gentry, S. Halevi, and VinodVaikuntanathan. “Fully Homomorphic Encryption over the Integers.”(EUROCRYPT 2010,http://eprint.iacr.org/2009/616)
  • This variant is not based on the lattice but has a similarstructure to the Regev03 encryption scheme [Reg04].
• [CMNT11-C] Jean-Sebastien Coron, Avradip Mandal, DavidNaccache, Mehdi Tibouchi: Fully Homomorphic Encryption over theIntegers with Shorter Public Keys. CRYPTO 2011
  • |pk| \in [1,800] MB
• [CNT12-EC] Jean-Sebastien Coron, David Naccache, MehdiTibouchi: Public Key Compression and Modulus Switching for FullyHomomorphic Encryption over the Integers. EUROCRYPT 2012

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Attacks orEstimations †

• [Ngu11-CANS] Phong Q. Nguyen: BreakingFully-Homomorphic-Encryption Challenges. CANS 2011
  • From his assessment, ...'s challenge is too optimistic.
• [CN12-EC] Yuanmi Chen, Phong Q. Nguyen: Faster Algorithms forApproximate Common Divisors: Breaking Fully-Homomorphic-EncryptionChallenges over the Integers. EUROCRYPT 2012
  • Attacking ???

• [ZPS12-ISPEC] Z. Zhang, T. Plantard and W. Susilo: On the CCA-1Security of Somewhat Homomorphic Encryption over the Integers.ISPEC 2012
• [ZPS11-ICISC] Z. Zhang, T. Plantard and W. Susilo: ReactionAttack on Outsourced Computing with Fully Homomorphic EncryptionSchemes. ICISC 2011

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Implementations †

• [OYKU10-IWSEC] N. Ogura, G. Yamamoto, T. Kobayashi, and S.Uchiyama. “An Improvement of Key Generation Algorithm for Gentry'sHomomorphic Encryption Scheme.” (IWSEC 2010)
• [GH11-EC] Craig Gentry, Shai Halevi: Implementing Gentry'sFully-Homomorphic Encryption Scheme. EUROCRYPT 2011
• [GH11-FOCS] Craig Gentry, Shai Halevi: Fully HomomorphicEncryption without Squashing Using Depth-3 Arithmetic Circuits.FOCS 2011
• [GHS12-PKC] Craig Gentry, Shai Halevi, Nigel P. Smart: BetterBootstrapping in Fully Homomorphic Encryption. PKC 2012
• [GHS12-EC] Craig Gentry, Shai Halevi, Nigel P. Smart: FullyHomomorphic Encryption with Polylog Overhead. EUROCRYPT 2012

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FromCode †

• [AAPS11-IMACC] Frederik Armknecht, Daniel Augot, LudovicPerret, Ahmad-Reza Sadeghi: On Constructing Homomorphic EncryptionSchemes from Coding Theory. IMA CC 2011, ePrint 2011/309
  • symmetric-key bounded-homomorphic encryption from code
  • they showed impossibility results.
• [BL11-eP] Andrej Bogdanov and Chin Ho Lee: Homomorphicencryption from codes. ePrint 2011/622
• ? Cryptanalysis of the Bogdanov-Lee Cryptosystem by GottfriedHerold
  • From Gauthier's talk at CBC 2012. See http://cbc2012.mat.dtu.dk/slides/Gauthier.pdf
• [GOT12-eP] Val\'erie Gauthier and Ayoub Otmani and Jean-PierreTillich: A Distinguisher-Based Attack of a Homomorphic EncryptionScheme Relying on Reed-Solomon Codes. ePrint 2012/168
  • cryptanalysis of [BL11-eP]
• [Bra12-eP-Whe] Zvika Brakerski: When Homomorphism Becomes aLiability. ePrint 2012/225
  • cryptanalysis of [BL11-eP]

Encryption CPU :https://hcrypt.com/shape-cpu/

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FromMQ? †

• Fellows and Koblitz: Polly Cracker.
• [AFFP11-AC] Martin R. Albrecht, Pooya Farshim, Jean-CharlesFaugere, Ludovic Perret: Polly Cracker, Revisited. ASIACRYPT2011
• [Her12-PKC] Gottfried Herold: Polly Cracker, Revisited,Revisited. PKC 2012

                     

Last-modified: 2012-08-28 (Tue) 15:00:31 (41d)

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