Page 424 - 《软件学报》2026年第1期
P. 424

曹金政 等: 格上困难问题量子求解算法综述                                                            421


                 [27]   Ramos-Calderer  S,  Bellini  E,  Latorre  JI,  Manzano  M,  Mateu  V.  Quantum  search  for  scaled  hash  function  preimages.  Quantum
                      Information Processing, 2021, 20(5): 180. [doi: 10.1007/s11128-021-03118-9]
                 [28]   Baek S, Kim J. Quantum rebound attacks on reduced-round aria-based hash functions. ETRI Journal, 2023, 45(3): 365–378. [doi: 10.
                      4218/etrij.2022-0032]
                 [29]   Hoffstein  J,  Pipher  J,  Silverman  JH.  NTRU:  A  ring-based  public  key  cryptosystem.  In:  Proc.  of  the  3rd  Int’l  Algorithmic  Number
                      Theory Symp. Portland: Springer, 1998. 267–288. [doi: 10.1007/BFb0054868]
                 [30]   Gentry C, Sahai A, Waters B. Homomorphic encryption from learning with errors: Conceptually-simpler, asymptotically-faster, attribute-
                      based. In: Proc. of the 33rd Annual Int’l Cryptology Conf. Santa Barbara: Springer, 2013. 75–92. [doi: 10.1007/978-3-642-40041-4_5]
                 [31]   Regev  O.  Quantum  computation  and  lattice  problems.  SIAM  Journal  on  Computing,  2004,  33(3):  738–760.  [doi:  10.1137/
                      S0097539703440678]
                 [32]   Aono Y, Nguyen PQ, Seito T, Shikata J. Lower bounds on lattice enumeration with extreme pruning. In: Proc. of the 38th Annual Int’l
                      Cryptology Conf. Santa Barbara: Springer, 2018. 608–637. [doi: 10.1007/978-3-319-96881-0_21]
                 [33]   May A, Nowakowski J. Too many hints—When LLL breaks LWE. In: Proc. of the 29th Int’l Conf. on the Theory and Application of
                      Cryptology and Information Security. Guangzhou: Springer, 2023. 106–137. [doi: 10.1007/978-981-99-8730-6_4]
                 [34]   Ajtai M, Kumar R, Sivakumar D. A sieve algorithm for the shortest lattice vector problem. In: Proc. of the 33rd Annual ACM Symp. on
                      Theory of Computing. Hersonissos: ACM, 2001. 601–610. [doi: 10.1145/380752.380857]
                 [35]   Micciancio D, Voulgaris P. Faster exponential time algorithms for the shortest vector problem. In: Proc. of the 21st Annual ACM-SIAM
                      Symp. on Discrete Algorithms. Austin: SIAM, 2010. 1468–1480. [doi: 10.1137/1.9781611973075.119]
                 [36]   Bi L, Lu XH, Wang KP. Research status and development trend of lattice sieving. Journal of Cryptologic Research, 2021, 8(5): 735–757
                      (in Chinese with English abstract). [doi: 10.13868/j.cnki.jcr.000474]
                 [37]   Pohst  M.  On  the  computation  of  lattice  vectors  of  minimal  length,  successive  minima  and  reduced  bases  with  applications.  ACM
                      SIGSAM Bulletin, 1981, 15(1): 37–44. [doi: 10.1145/1089242.1089247]
                 [38]   Nguyen PQ, Vallèe B. The LLL Algorithm: Survey and Applications. Berlin: Springer, 2010. [doi: 10.1007/978-3-642-02295-1]
                 [39]   Lenstra  AK,  Lenstra  Jr  HW,  Lovász  L.  Factoring  polynomials  with  rational  coefficients.  Mathematische  Annalen,  1982,  261(4):
                      515–534. [doi: 10.1007/BF01457454]
                 [40]   Schnorr  CP,  Euchner  M.  Lattice  basis  reduction:  Improved  practical  algorithms  and  solving  subset  sum  problems.  Mathematical
                      Programming, 1994, 66(1–3): 181–199. [doi: 10.1007/BF01581144]
                 [41]   Esser A, Heuer F, Kübler R, May A, Sohler C. Dissection-BKW. In: Proc. of the 38th Annual Int’l Cryptology Conf. Santa Barbara:
                      Springer, 2018. 638–666. [doi: 10.1007/978-3-319-96881-0_22]
                 [42]   Albrecht MR, Shen YX. Quantum augmented dual attack. IACR Cryptology ePrint Archive, 2022.656.
                 [43]   Liu HL, Yu Y. A non-heuristic approach to time-space tradeoffs and optimizations for BKW. In: Proc. of the 28th Int’l Conf. on the
                      Theory  and  Application  of  Cryptology  and  Information  Security.  Taipei:  Springer,  2022.  741–770.  [doi:  10.1007/978-3-031-22969-
                      5_25]
                 [44]   Chen YL. Quantum algorithms for lattice problems. IACR Cryptology ePrint Archive, 2024.555.
                 [45]   Fluhrer SR. Quantum cryptanalysis of NTRU. IACR Cryptology ePrint Archive, 2015.676.
                 [46]   Laaji EH, Azizi A, Ezzouak S. Two quantum attack algorithms against NTRU when the private key and plaintext are codified in ternary
                      polynomials.  In:  Serrhini  M,  Silva  C,  Aljahdali  S,  eds.  Innovation  in  Information  Systems  and  Technologies  to  Support  Learning
                      Research. Cham: Springer, 2019. 551–562. [doi: 10.1007/978-3-030-36778-7_61]
                 [47]   Dong J. The quantum algorithm analysis of NTRU cryptography and the research of quantum lattice sieving algorithm [MS. Thesis].
                      Beijing: Beijing University of Posts and Telecommunications, 2021 (in Chinese with English abstract). [doi: 10.26969/d.cnki.gbydu.
                      2021.001999]
                 [48]   Laarhoven T, Mosca M, van de Pol J. Solving the shortest vector problem in lattices faster using quantum search. In: Proc. of the 5th Int’l
                      Conf. on Post-quantum Cryptography. Limoges: Springer, 2013. 83–101. [doi: 10.1007/978-3-642-38616-9_6]
                 [49]   Laarhoven T, Mosca M, van de Pol J. Finding shortest lattice vectors faster using quantum search. Designs, Codes and Cryptography,
                      2015, 77(2): 375–400. [doi: 10.1007/s10623-015-0067-5]
                 [50]   Becker A, Laarhoven T. Efficient (ideal) lattice sieving using cross-polytope LSH. In: Proc. of the 8th Int’l Conf. on Cryptology in
                      Africa. Fes: Springer, 2016. 3–23. [doi: 10.1007/978-3-319-31517-1_1]
                 [51]   Becker A, Ducas L, Gama N, Laarhoven T. New directions in nearest neighbor searching with applications to lattice sieving. In: Proc. of
                      the 27th Annual ACM-SIAM Symp. on Discrete Algorithms. Arlington: Society for Industrial and Applied Mathematics, 2016. 10–24.
                      [doi: 10.5555/2884435.2884437]
   419   420   421   422   423   424   425   426   427   428   429