The variants of lattice-based cryptosystems.

crypt

See also g:lab:keyword:現代暗号史_格子

with worst-case/average-case reductions

without worst-case/average-case reductions

  • GGH *11
    • GGH-Micciancio *12
    • GGH-PJH *13
  • NTRU *14
    • NTRU-BS *15
    • MaTRU *16
    • Others...
  • Ajtai05 *17
  • Cai-Cusick *19
    • It is a variant of AD TypeIII without an a/w reduction.
  • Fischlin-Seifert *20

*1:M. Ajtai, C. Dwork. "A public-key cryptosystem with worst-case/average-case equivalence." (STOC 1997, ECCC 1996)

*2:O. Goldreich, S. Goldwasser, and S. Halevi. "Eliminating decryption errors in the Ajtai-Dwork cryptosystem." (CRYPTO 1997, ECCC 1997)

*3:A. Kawachi, K. Tanaka, K. Xagawa. "Multi-Bit Public-Key Cryptosystems Based on Lattice Problems." (PKC 2007)

*4:M. Ajtai, C. Dwork. "The First and Fourth Public-Key Cryptosystems with Worst-Case/Average-Case Equivalence." (ECCC TR07-097)

*5:O. Regev. "New Lattice Based Cryptographic Constructions." (STOC 2003, J. of ACM 2004)

*6:A. Kawachi, K. Tanaka, K. Xagawa. "Multi-Bit Public-Key Cryptosystems Based on Lattice Problems." (PKC 2007)

*7:O. Regev. "On Lattices, Learnin with Errors, Random Linear Codes, and Cryptography." (STOC 2005)

*8:A. Kawachi, K. Tanaka, K. Xagawa. "Multi-Bit Public-Key Cryptosystems Based on Lattice Problems." (PKC 2007)

*9:C. Peikert, B. Waters. "Lossy Trapdoor Functions and Their Applications." (ePrint 2007/279)

*10:C. Peikert, V. Vaikuntanathan, B. Waters "A Framework for Efficient and Composable Oblivious Transfer." (ePrint 2007/348)

*11:O. Goldreich, S. Goldwasser, and S. Halevi. "Public-key cryptosystem from lattice reduction problems." (CRYPTO 1997, ECCC 1997?)

*12:D. Micciancio. "Improving Lattice Based Cryptosystems Using the Hermite Normal Form." (CaLC 2001)

*13:S.-H. Paeng, B. E. Jung, K.-C. Ha. "A Lattice Based Public Key Cryptosystem Using Polynomial Representations" (PKC 2003)

*14:J. Hoffstein, J. Pipher, J. H. Silverman. "NTRU: A Ring-Based Public Key Cryptosystem." (ANTS-III)

*15:W. D. Banks, I. Shparlinski. "A Variant of NTRU with Non-invertible Polynomials." (INDOCRYPT 2002)

*16:M. Coglianese, B.-M. Goi. "MaTRU: A New NTRU-Based Cryptosystem." (INDCRYPT 2005)

*17:M. Ajtai. "Representing hard lattices with O(n \log n) bits." (STOC 2005)

*18:A. Kawachi, K. Tanaka, K. Xagawa. "Multi-Bit Public-Key Cryptosystems Based on Lattice Problems." (PKC 2007)

*19:J-Y. Cai, T. Cusick. "A Lattice-Based Public-Key Cryptosystem." (SAC 1998, Inf. Comput. Vol.151(1999) )

*20:R. Fischlin, J.-P. Seifert. "Tensor-based Trapdoors for CVP and their Application to Public Key Cryptography." (WCC 1999)