% Bibliography of the 2877 items from 2009 counted in the Cryptanalytic Effort study. % Generated 2026-10-11 by pipeline/build_bibliography.py from data/export/combined_included.csv. % Custom fields: classes, category, rationale, vetted, peerreviewed, quantum, sources, studyid. @phdthesis{openalex:W2268374210, author = {Jin-Su Kim and 김진수}, title = {{(A) hybrid attack using splitting systems against NTRU = NTRU에 대한 splitting system을 이용한 hybrid 공격}}, school = {Dissertation (institution not recorded)}, year = {2009}, url = {https://openalex.org/W2268374210}, classes = {Lattices 1}, category = {A}, rationale = {Hybrid attack on NTRU using splitting systems; title only.}, vetted = {no}, peerreviewed = {no}, quantum = {no}, sources = {openalex_phrase}, studyid = {W2268374210}, countyear = {2009}, venuenote = {published venue resolved from openalex W2268374210 type dissertation, no host (confidence 0.70)} } @article{eprint:2009-619, author = {Charles Bouillaguet and Pierre-Alain Fouque and Antoine Joux and Joana Treger}, title = {{A Family of Weak Keys in HFE (and the Corresponding Practical Key-Recovery)}}, eprint = {2009/619}, eprinttype = {iacr}, eprintclass = {Public-key cryptography}, journal = {Journal of Mathematical Cryptology}, note = {Also Cryptology {ePrint} Archive, Paper 2009/619}, year = {2012}, doi = {10.1515/jmc.2011.012}, url = {https://eprint.iacr.org/2009/619}, classes = {Multivariate 1}, category = {C}, rationale = {Weak HFE keys with ground-field coefficients; practical key recovery via IP.}, vetted = {yes}, peerreviewed = {yes}, quantum = {no}, sources = {eprint}, studyid = {2009/619}, countyear = {2009}, venuenote = {published venue resolved from dblp journals/jmc/BouillaguetFJT12 (confidence 0.95)} } @inproceedings{openalex:W2162030009, author = {Dimitrios Meintanis and Ioannis Papaefstathiou}, title = {{A module-based partial reconfiguration design for solving sparse linear systems over GF(2)}}, booktitle = {2009 International Conference on Field-Programmable Technology}, year = {2009}, doi = {10.1109/fpt.2009.5377677}, url = {https://doi.org/10.1109/fpt.2009.5377677}, classes = {Factoring/FF-DLP 1}, category = {A}, rationale = {FPGA design speeding NFS linear algebra (block Wiedemann) over GF(2).}, vetted = {no}, peerreviewed = {yes}, quantum = {no}, sources = {openalex_phrase}, studyid = {W2162030009}, countyear = {2009}, venuenote = {published venue resolved from crossref 10.1109/fpt.2009.5377677 (confidence 0.95)} } @inproceedings{dblp:conf-pkc-Aono09, author = {Yoshinori Aono}, title = {{A New Lattice Construction for Partial Key Exposure Attack for RSA}}, booktitle = {PKC 2009}, year = {2009}, doi = {10.1007/978-3-642-00468-1_3}, url = {https://doi.org/10.1007/978-3-642-00468-1_3}, classes = {}, category = {A}, rationale = {New Coppersmith lattice construction for RSA partial key exposure.}, vetted = {yes}, peerreviewed = {yes}, quantum = {no}, sources = {dblp, zbmath}, studyid = {dblp:conf/pkc/Aono09}, countyear = {2009}, venuenote = {published venue resolved from dblp conf/pkc/Aono09 [+crossref,dblp-self] (confidence 1.00)} } @misc{openalex:W2218640666, author = {Alexander I. Kruppa}, title = {{A Software Implementation of ECM for NFS}}, howpublished = {HAL}, year = {2009}, url = {https://openalex.org/W2218640666}, classes = {Factoring/FF-DLP 1}, category = {A}, rationale = {High-throughput ECM for NFS cofactorization.}, vetted = {no}, peerreviewed = {no}, quantum = {no}, sources = {openalex_phrase}, studyid = {W2218640666}, countyear = {2009}, venuenote = {published venue resolved from openalex W2218640666 S4306402512 (confidence 0.80)} } @article{zbmath:1220.11155, author = {Babul', O. V.}, title = {{About sieving methods in lattice algorithms of number fields}}, journal = {Trudy Instituta Matematiki}, year = {2009}, url = {https://zbmath.org/?q=an:1220.11155}, classes = {Factoring/FF-DLP 1}, category = {A}, rationale = {Discusses line, lattice and continued-fraction sieving in NFS.}, vetted = {no}, peerreviewed = {yes}, quantum = {no}, sources = {zbmath}, studyid = {zb:1220.11155}, countyear = {2009}, venuenote = {published venue resolved from zbmath 1220.11155 (confidence 0.90)} } @article{dblp:journals-jmc-BourgeoisF09, author = {Gerald Bourgeois and Jean-Charles Faugère}, title = {{Algebraic attack on NTRU using Witt vectors and Gröbner bases}}, journal = {Journal of Mathematical Cryptology}, year = {2009}, doi = {10.1515/jmc.2009.011}, url = {https://doi.org/10.1515/jmc.2009.011}, classes = {Lattices 1}, category = {A}, rationale = {Witt-vector Groebner algebraic attack on NTRU with complexity analysis.}, vetted = {yes}, peerreviewed = {yes}, quantum = {no}, sources = {dblp, openalex_phrase, zbmath}, studyid = {dblp:journals/jmc/BourgeoisF09}, countyear = {2009}, venuenote = {published venue resolved from dblp journals/jmc/BourgeoisF09 [+crossref,dblp-self] (confidence 1.00)} } @article{dblp:journals-corr-abs-0905-2177, author = {Andreas Enge and Pierrick Gaudry and Emmanuel Thomé}, title = {{An $L (1/3)$ Discrete Logarithm Algorithm for Low Degree Curves}}, journal = {Journal of Cryptology}, year = {2011}, doi = {10.48550/arxiv.0905.2177}, url = {https://doi.org/10.48550/arxiv.0905.2177}, classes = {ECDLP 1}, category = {A}, rationale = {L(1/3) index calculus for Jacobians of low-degree plane curves.}, vetted = {yes}, peerreviewed = {yes}, quantum = {no}, sources = {dblp, openalex_phrase}, studyid = {dblp:journals/corr/abs-0905-2177}, countyear = {2009}, venuenote = {published venue resolved from dblp journals/joc/EngeGT11 (retitled? sim 0.965: (1/3) Discrete Logarithm Algorithm for Low Degree Curves) (confidence 0.85)} } @inproceedings{openalex:W176147980, author = {Steven D. Galbraith⋆ and Raminder S. Ruprai}, title = {{An Improvement to the Gaudry-Schost Algorithm for Multidimensional Discrete Logarithm Problems}}, booktitle = {IMA Cryptography and Coding (IMACC) 2009}, year = {2009}, doi = {10.1007/978-3-642-10868-6_22}, url = {https://doi.org/10.1007/978-3-642-10868-6_22}, classes = {ECDLP 0.5, Factoring/FF-DLP 0.5}, category = {A}, rationale = {Improved Gaudry-Schost algorithm for multidimensional DLP.}, vetted = {no}, peerreviewed = {yes}, quantum = {no}, sources = {openalex, zbmath}, studyid = {W176147980}, countyear = {2009}, venuenote = {published venue resolved from dblp conf/ima/GalbraithR09 [+crossref,dblp-title] (confidence 0.98)} } @article{dblp:journals-siamcomp-NguyenS09, author = {Phong Q. Nguyen and Damien Stehlé}, title = {{An LLL Algorithm with Quadratic Complexity}}, journal = {SIAM Journal on Computing}, year = {2009}, doi = {10.1137/070705702}, url = {https://doi.org/10.1137/070705702}, classes = {Lattices 1}, category = {A}, rationale = {L2 floating-point LLL with quadratic complexity.}, vetted = {yes}, peerreviewed = {yes}, quantum = {no}, sources = {dblp, openalex_snowball}, studyid = {dblp:journals/siamcomp/NguyenS09}, countyear = {2009}, venuenote = {published venue resolved from dblp journals/siamcomp/NguyenS09 [+crossref,dblp-self] (confidence 1.00)} } @article{openalex:W4241339619, author = {Dmitri Maslov and Jimson Mathew and Donny Cheung and Dhiraj K. Pradhan}, title = {{An O(m 2 )-depth quantum algorithm for the elliptic curve discrete logarithm problem over GF(2 m ) a}}, journal = {Quantum Information \& Computation}, year = {2009}, doi = {10.5555/2011814.2011818}, url = {https://doi.org/10.5555/2011814.2011818}, classes = {ECDLP 1}, category = {B}, rationale = {O(m\^{}2)-depth quantum circuit for binary-field ECDLP.}, vetted = {no}, peerreviewed = {yes}, quantum = {yes}, sources = {openalex_phrase, zbmath}, studyid = {W4241339619}, countyear = {2009}, venuenote = {published venue resolved from openalex W4241339619 S41034432 (confidence 0.80)} } @incollection{openalex:W2738987452, author = {R. Balasubramanian and Gagan Garg and C. E. Veni Madhavan}, title = {{Analysis of the Lattice Sieve}}, booktitle = {Number Theory and Applications}, year = {2009}, doi = {10.1007/978-93-86279-46-0_1}, url = {https://doi.org/10.1007/978-93-86279-46-0_1}, classes = {Factoring/FF-DLP 1}, category = {A}, rationale = {Analysis of line vs lattice sieving in NFS.}, vetted = {no}, peerreviewed = {no}, quantum = {no}, sources = {openalex_phrase, zbmath}, studyid = {W2738987452}, countyear = {2009}, venuenote = {published venue resolved from crossref 10.1007/978-93-86279-46-0\_1 (confidence 0.95)} } @inproceedings{eprint:2009-221, author = {David Jao and Kayo Yoshida}, title = {{Boneh-Boyen signatures and the Strong Diffie-Hellman problem}}, eprint = {2009/221}, eprinttype = {iacr}, eprintclass = {Public-key cryptography}, booktitle = {Pairing 2009}, note = {Also Cryptology {ePrint} Archive, Paper 2009/221}, year = {2009}, doi = {10.1007/978-3-642-03298-1_1}, url = {https://eprint.iacr.org/2009/221}, classes = {ECDLP 1}, category = {A}, rationale = {BB forgery equivalent to q-SDH; Cheon-type key recovery faster than rho on pairing curves.}, vetted = {yes}, peerreviewed = {yes}, quantum = {no}, sources = {eprint}, studyid = {2009/221}, countyear = {2009}, venuenote = {published venue resolved from dblp conf/pairing/JaoY09 [+dblp-title,eprint-pubinfo] (confidence 0.98)} } @misc{eprint:2009-541, author = {Daniel V. Bailey and Lejla Batina and Daniel J. Bernstein and Peter Birkner and Joppe W. Bos and Hsieh-Chung Chen and Chen-Mou Cheng and Gauthier van Damme and Giacomo de Meulenaer and Luis Julian Dominguez Perez and Junfeng Fan and Tim Güneysu and Frank Gurkaynak and Thorsten Kleinjung and Tanja Lange and Nele Mentens and Ruben Niederhagen and Christof Paar and Francesco Regazzoni and Peter Schwabe and Leif Uhsadel and Anthony Van Herrewege and Bo-Yin Yang}, title = {{Breaking ECC2K-130}}, howpublished = {Cryptology {ePrint} Archive, Paper 2009/541}, eprint = {2009/541}, eprinttype = {iacr}, eprintclass = {Implementation}, year = {2009}, url = {https://eprint.iacr.org/2009/541}, classes = {ECDLP 1}, category = {D}, rationale = {Cost analysis and implementations for Pollard rho on ECC2K-130; computation not completed.}, vetted = {yes}, peerreviewed = {no}, quantum = {no}, sources = {eprint}, studyid = {2009/541}, countyear = {2009} } @article{openalex:W4245259404, author = {Kazumaro Aoki and Hiroki R. Ueda}, title = {{Bucket Sieving}}, journal = {IEICE Transactions}, year = {2009}, doi = {10.1587/transfun.e92.a.1845}, url = {https://doi.org/10.1587/transfun.e92.a.1845}, classes = {Factoring/FF-DLP 1}, category = {A}, rationale = {Cache-efficient bucket sieving for NFS.}, vetted = {no}, peerreviewed = {yes}, quantum = {no}, sources = {openalex_phrase}, studyid = {W4245259404}, countyear = {2009}, venuenote = {published venue resolved from dblp journals/ieicet/AokiU09 [+crossref,dblp-title,openalex] (confidence 1.00)} } @inproceedings{dblp:conf-acns-HirschhornHHW09, author = {Philip S. Hirschhorn and Jeffrey Hoffstein and Nick Howgrave-Graham and William Whyte}, title = {{Choosing NTRUEncrypt Parameters in Light of Combined Lattice Reduction and MITM Approaches}}, booktitle = {ACNS 2009}, year = {2009}, doi = {10.1007/978-3-642-01957-9_27}, url = {https://doi.org/10.1007/978-3-642-01957-9_27}, classes = {Lattices 1}, category = {D}, rationale = {NTRUEncrypt parameter selection against hybrid lattice/MITM attack.}, vetted = {yes}, peerreviewed = {yes}, quantum = {no}, sources = {dblp}, studyid = {dblp:conf/acns/HirschhornHHW09}, countyear = {2009}, venuenote = {published venue resolved from dblp conf/acns/HirschhornHHW09 [+crossref,dblp-self] (confidence 1.00)} } @misc{eprint:2009-613, author = {Tsutomu Iijima and Fumiyuki Momose and Jinhui Chao}, title = {{Classification of Elliptic/hyperelliptic Curves with Weak Coverings against GHS Attack without Isogeny Condition}}, howpublished = {Cryptology {ePrint} Archive, Paper 2009/613}, eprint = {2009/613}, eprinttype = {iacr}, eprintclass = {Public-key cryptography}, year = {2009}, url = {https://eprint.iacr.org/2009/613}, classes = {ECDLP 1}, category = {C}, rationale = {Classifies curves with weak coverings vulnerable to GHS Weil descent.}, vetted = {yes}, peerreviewed = {no}, quantum = {no}, sources = {eprint}, studyid = {2009/613}, countyear = {2009} } @article{eprint:2009-037, author = {M. Jason Hinek and Charles C. Y. Lam}, title = {{Common Modulus Attacks on Small Private Exponent RSA and Some Fast Variants (in Practice)}}, eprint = {2009/037}, eprinttype = {iacr}, eprintclass = {Public-key cryptography}, journal = {Journal of Mathematical Cryptology}, note = {Also Cryptology {ePrint} Archive, Paper 2009/037}, year = {2010}, doi = {10.1515/jmc.2010.003}, url = {https://eprint.iacr.org/2009/037}, classes = {Factoring/FF-DLP 1}, category = {C}, rationale = {Common-modulus small-exponent RSA attacks (continued fraction, lattice) and variants.}, vetted = {yes}, peerreviewed = {yes}, quantum = {no}, sources = {eprint}, studyid = {2009/037}, countyear = {2009}, venuenote = {published venue resolved from dblp journals/jmc/HinekL10 (confidence 0.95)} } @article{eprint:2009-245, author = {Naoki Ogura and Shigenori Uchiyama}, title = {{Cryptanalysis of the Birational Permutation Signature Scheme over a Non-commutative Ring}}, eprint = {2009/245}, eprinttype = {iacr}, eprintclass = {Public-key cryptography}, journal = {JSIAM Letters}, note = {Also Cryptology {ePrint} Archive, Paper 2009/245}, year = {2010}, doi = {10.14495/jsiaml.2.85}, url = {https://eprint.iacr.org/2009/245}, classes = {Multivariate 1}, category = {C}, rationale = {Structural key-recovery on non-commutative birational scheme and a class of Rainbow-type multivariate schemes.}, vetted = {yes}, peerreviewed = {yes}, quantum = {no}, sources = {eprint}, studyid = {2009/245}, countyear = {2009}, venuenote = {published venue resolved from dblp journals/jsiaml/OguraU10 [+dblp-fuzzy,dblp-title] (confidence 0.98)} } @inproceedings{eprint:2009-452, author = {Christian Wieschebrink}, title = {{Cryptanalysis of the Niederreiter Public Key Scheme Based on GRS Subcodes}}, eprint = {2009/452}, eprinttype = {iacr}, eprintclass = {Public-key cryptography}, booktitle = {PQCrypto 2010}, note = {Also Cryptology {ePrint} Archive, Paper 2009/452}, year = {2010}, doi = {10.1007/978-3-642-12929-2_5}, url = {https://eprint.iacr.org/2009/452}, classes = {Syndrome decoding 1}, category = {C}, rationale = {Structural polynomial-time key recovery on GRS-subcode Niederreiter.}, vetted = {yes}, peerreviewed = {yes}, quantum = {no}, sources = {eprint}, studyid = {2009/452}, countyear = {2009}, venuenote = {published venue resolved from dblp conf/pqcrypto/Wieschebrink10 (confidence 0.95)} } @article{openalex:W2417659390, author = {Marta Chinnici and Salvatore Cuomo and Maurizio Laporta and Alberto Pizzirani and S. Migliori}, title = {{CUDA based implementation of parallelized Pollard’s Rho algorithm for ECDLP}}, journal = {CiiT international journal of data mining and knowledge engineering}, year = {2015}, url = {https://openalex.org/W2417659390}, classes = {ECDLP 1}, category = {A}, rationale = {GPU parallel Pollard rho implementation for ECDLP, speed-focused.}, vetted = {no}, peerreviewed = {yes}, quantum = {no}, sources = {openalex_phrase}, studyid = {W2417659390}, countyear = {2009}, venuenote = {published venue resolved from openalex W2417659390 S2764364946 (confidence 0.80)} } @article{zbmath:1572.11178, author = {Pankratova, I. A.}, title = {{Discrete logarithm problem in subgroups of prime order}}, journal = {Prikladnaya Diskretnaya Matematika}, year = {2009}, url = {https://zbmath.org/?q=an:1572.11178}, classes = {Factoring/FF-DLP 1}, category = {A}, rationale = {Modified Adleman index calculus for DL in prime-order subgroups.}, vetted = {no}, peerreviewed = {yes}, quantum = {no}, sources = {zbmath}, studyid = {zb:1572.11178}, countyear = {2009}, venuenote = {published venue resolved from zbmath 1572.11178 (confidence 0.90)} } @misc{openalex:W562888130, author = {Pavol Zajac}, title = {{Discrete Logarithms and Degree Six Number Field Sieve: A practical approach}}, howpublished = {Medical Entomology and Zoology}, year = {2009}, url = {https://openalex.org/W562888130}, classes = {Factoring/FF-DLP 1}, category = {A}, rationale = {Title only: practical degree-six NFS for discrete logarithms.}, vetted = {no}, peerreviewed = {no}, quantum = {no}, sources = {openalex_phrase}, studyid = {W562888130}, countyear = {2009} } @inproceedings{openalex:W2156390856, author = {Marek Aleksander and Grzegorz Litawa and Volodymyr Karpinskyi}, title = {{Distributed computing system which solve an elliptic curve discrete logarithm problem}}, booktitle = {International Conference on Experience of Designing and Applications of CAD Systems in Microelectronics}, year = {2009}, url = {https://openalex.org/W2156390856}, classes = {ECDLP 1}, category = {A}, rationale = {Distributed CPU/FPGA parallel Pollard rho system for ECDLP with time estimates.}, vetted = {no}, peerreviewed = {yes}, quantum = {no}, sources = {openalex_phrase}, studyid = {W2156390856}, countyear = {2009}, venuenote = {published venue resolved from openalex W3144258647 S4306419456 (confidence 0.80)} } @article{eprint:2009-236, author = {Fumiyuki Momose and Jinhui Chao}, title = {{Elliptic curves with weak coverings over cubic extensions of finite fields with odd characteristics}}, eprint = {2009/236}, eprinttype = {iacr}, eprintclass = {Public-key cryptography}, journal = {Journal of the Ramanujan Mathematical Society}, note = {Also Cryptology {ePrint} Archive, Paper 2009/236}, year = {2009}, url = {https://eprint.iacr.org/2009/236}, classes = {ECDLP 1}, category = {C}, rationale = {Classifies elliptic curves over cubic extensions weak under GHS Weil descent.}, vetted = {yes}, peerreviewed = {yes}, quantum = {no}, sources = {eprint}, studyid = {2009/236}, countyear = {2009}, venuenote = {published venue resolved from eprint pubinfo: Journal of the Ramanujan Mathematical Society (JRMS) (confidence 0.75)} } @inproceedings{openalex:W1983937072, author = {Chang Liu and Chi Yang}, title = {{Factoring RSA modulo N with high bits of p known revisited}}, booktitle = {2009 IEEE International Symposium on IT in Medicine \& Education}, year = {2009}, doi = {10.1109/itime.2009.5236369}, url = {https://doi.org/10.1109/itime.2009.5236369}, classes = {}, category = {A}, rationale = {Improved bounds for factoring RSA with known high bits of p and small d.}, vetted = {no}, peerreviewed = {yes}, quantum = {no}, sources = {openalex_snowball}, studyid = {W1983937072}, countyear = {2009}, venuenote = {published venue resolved from crossref 10.1109/itime.2009.5236369 (confidence 0.95)} } @inproceedings{eprint:2009-323, author = {Eric Brier and David Naccache and Mehdi Tibouchi}, title = {{Factoring Unbalanced Moduli with Known Bits}}, eprint = {2009/323}, eprinttype = {iacr}, eprintclass = {Foundations}, booktitle = {ICISC 2009}, note = {Also Cryptology {ePrint} Archive, Paper 2009/323}, year = {2009}, doi = {10.1007/978-3-642-14423-3_5}, url = {https://eprint.iacr.org/2009/323}, classes = {Factoring/FF-DLP 1}, category = {C}, rationale = {LLL/Coppersmith factoring of unbalanced RSA moduli given known bits of p.}, vetted = {yes}, peerreviewed = {yes}, quantum = {no}, sources = {eprint}, studyid = {2009/323}, countyear = {2009}, venuenote = {published venue resolved from dblp conf/icisc/BrierNT09 (confidence 0.95)} } @inproceedings{dblp:journals-eccc-VoulgarisM09, author = {Daniele Micciancio and Panagiotis Voulgaris}, title = {{Faster Exponential Time Algorithms for the Shortest Vector Problem}}, booktitle = {SODA 2010}, year = {2010}, doi = {10.1137/1.9781611973075.119}, url = {https://doi.org/10.1137/1.9781611973075.119}, classes = {Lattices 1}, category = {A}, rationale = {Faster exponential-time exact SVP algorithms (ListSieve, improved AKS).}, vetted = {yes}, peerreviewed = {yes}, quantum = {no}, sources = {dblp, openalex_phrase, zbmath}, studyid = {dblp:journals/eccc/VoulgarisM09}, countyear = {2009}, venuenote = {published venue resolved from dblp conf/soda/MicciancioV10 [+crossref,dblp-title] (confidence 0.98)} } @incollection{dblp:series-isc-Stehle10, author = {Damien Stehlé}, title = {{Floating-Point LLL: Theoretical and Practical Aspects}}, booktitle = {The LLL Algorithm}, year = {2009}, doi = {10.1007/978-3-642-02295-1_5}, url = {https://doi.org/10.1007/978-3-642-02295-1_5}, classes = {Lattices 1}, category = {A}, rationale = {Floating-point LLL theory and practice.}, vetted = {yes}, peerreviewed = {no}, quantum = {no}, sources = {dblp, openalex_snowball, zbmath}, studyid = {dblp:series/isc/Stehle10}, countyear = {2009}, venuenote = {published venue resolved from dblp series/isc/Stehle10 [+crossref,dblp-self] (confidence 1.00)} } @article{dblp:journals-amco-SarkarM09, author = {Santanu Sarkar and Subhamoy Maitra}, title = {{Further results on implicit factoring in polynomial time}}, journal = {Advances in Mathematics of Communications}, year = {2009}, doi = {10.3934/amc.2009.3.205}, url = {https://doi.org/10.3934/amc.2009.3.205}, classes = {}, category = {A}, rationale = {Implicit factoring of RSA moduli with shared bits via lattices.}, vetted = {yes}, peerreviewed = {yes}, quantum = {no}, sources = {dblp, zbmath}, studyid = {dblp:journals/amco/SarkarM09}, countyear = {2009}, venuenote = {published venue resolved from dblp journals/amco/SarkarM09 [+crossref,dblp-self] (confidence 1.00)} } @article{zbmath:1301.14016, author = {Daghigh, H. and Bahramian, M.}, title = {{Generalized Jacobian and discrete logarithm problem on elliptic curves}}, journal = {Iranian Journal of Mathematical Sciences and Informatics}, year = {2009}, url = {https://zbmath.org/?q=an:1301.14016}, classes = {ECDLP 0.7, Factoring/FF-DLP 0.3}, category = {C}, rationale = {Reduces ECDLP on E[n] to F\_q\^{}* DLP via generalized Jacobian.}, vetted = {no}, peerreviewed = {yes}, quantum = {no}, sources = {zbmath}, studyid = {zb:1301.14016}, countyear = {2009}, venuenote = {published venue resolved from zbmath 1301.14016 (confidence 0.90)} } @inproceedings{dblp:conf-issac-MorelSV09, author = {Ivan Morel and Damien Stehlé and Gilles Villard}, title = {{H-LLL: using householder inside LLL}}, booktitle = {ISSAC 2009}, year = {2009}, doi = {10.1145/1576702.1576740}, url = {https://doi.org/10.1145/1576702.1576740}, classes = {Lattices 1}, category = {A}, rationale = {H-LLL: Householder-based floating-point LLL variant.}, vetted = {yes}, peerreviewed = {yes}, quantum = {no}, sources = {dblp}, studyid = {dblp:conf/issac/MorelSV09}, countyear = {2009}, venuenote = {published venue resolved from dblp conf/issac/MorelSV09 [+crossref,dblp-self] (confidence 1.00)} } @inproceedings{dblp:conf-stoc-MontenegroT09, author = {Ravi Montenegro and Prasad Tetali}, title = {{How long does it take to catch a wild kangaroo?}}, booktitle = {STOC 2009}, year = {2009}, doi = {10.1145/1536414.1536490}, url = {https://doi.org/10.1145/1536414.1536490}, classes = {ECDLP 0.5, Factoring/FF-DLP 0.5}, category = {A}, rationale = {Rigorous runtime analysis of Pollard kangaroo for interval DLP.}, vetted = {yes}, peerreviewed = {yes}, quantum = {no}, sources = {dblp}, studyid = {dblp:conf/stoc/MontenegroT09}, countyear = {2009}, venuenote = {published venue resolved from dblp conf/stoc/MontenegroT09 [+crossref,dblp-self] (confidence 1.00)} } @article{dblp:journals-jmc-BettaleFP09, author = {Luk Bettale and Jean-Charles Faugère and Ludovic Perret}, title = {{Hybrid approach for solving multivariate systems over finite fields}}, journal = {Journal of Mathematical Cryptology}, year = {2009}, doi = {10.1515/jmc.2009.009}, url = {https://doi.org/10.1515/jmc.2009.009}, classes = {Multivariate 1}, category = {A}, rationale = {Hybrid Groebner/exhaustive MQ solving; breaks TRMS and UOV parameters.}, vetted = {yes}, peerreviewed = {yes}, quantum = {no}, sources = {dblp, openalex_phrase}, studyid = {dblp:journals/jmc/BettaleFP09}, countyear = {2009}, venuenote = {published venue resolved from dblp journals/jmc/BettaleFP09 [+crossref,dblp-self] (confidence 1.00)} } @article{openalex:W1940355719, author = {R. Padmavathy and Chakravarthy Bhagvati}, title = {{Improved random method using smooth numbers over Zp}}, journal = {International journal of applied mathematics and computation}, year = {2009}, doi = {10.0000/ijamc.2010.2.3.78}, url = {https://doi.org/10.0000/ijamc.2010.2.3.78}, classes = {Factoring/FF-DLP 1}, category = {A}, rationale = {Improved index calculus smoothness step for prime-field DLP, experimental speedup.}, vetted = {no}, peerreviewed = {yes}, quantum = {no}, sources = {openalex_phrase}, studyid = {W1940355719}, countyear = {2009}, venuenote = {published venue resolved from openalex W1940355719 S2764701313 (confidence 0.80)} } @article{dblp:journals-jsc-Gaudry09, author = {Pierrick Gaudry}, title = {{Index calculus for abelian varieties of small dimension and the elliptic curve discrete logarithm problem}}, journal = {Journal of Symbolic Computation}, year = {2009}, doi = {10.1016/j.jsc.2008.08.005}, url = {https://doi.org/10.1016/j.jsc.2008.08.005}, classes = {}, category = {A}, rationale = {Index calculus on abelian varieties; ECDLP over small extensions faster than rho.}, vetted = {yes}, peerreviewed = {yes}, quantum = {no}, version = {same work as eprint:2004-073; counted there, weight 0 here}, sources = {dblp, zbmath}, studyid = {dblp:journals/jsc/Gaudry09}, countyear = {2009}, venuenote = {published venue resolved from dblp journals/jsc/Gaudry09 [+crossref,dblp-self] (confidence 1.00)} } @misc{eprint:2009-589, author = {Christiane Peters}, title = {{Information-set decoding for linear codes over Fq}}, howpublished = {Cryptology {ePrint} Archive, Paper 2009/589}, eprint = {2009/589}, eprinttype = {iacr}, eprintclass = {Public-key cryptography}, year = {2009}, url = {https://eprint.iacr.org/2009/589}, classes = {Syndrome decoding 1}, category = {A}, rationale = {Generalizes Stern ISD to codes over Fq with complexity analysis.}, vetted = {yes}, peerreviewed = {no}, quantum = {no}, sources = {eprint}, studyid = {2009/589}, countyear = {2009} } @article{openalex:W2155552496, author = {Boris S. Verkhov}, title = {{Integer Factorization: Solution via Algorithm for Constrained Discrete Logarithm Problem}}, journal = {Journal of Computer Science}, year = {2009}, doi = {10.3844/jcssp.2009.674.679}, url = {https://doi.org/10.3844/jcssp.2009.674.679}, classes = {Factoring/FF-DLP 1}, category = {A}, rationale = {Factoring algorithm via constrained DLP, O(n\^{}(1/3)); weak but an algorithm paper.}, vetted = {no}, peerreviewed = {yes}, quantum = {no}, sources = {openalex_phrase}, studyid = {W2155552496}, countyear = {2009}, venuenote = {published venue resolved from crossref 10.3844/jcssp.2009.674.679 [+crossref,openalex] (confidence 0.98)} } @phdthesis{dblp:phd-basesearch-Bulens09, author = {Philippe Bulens}, title = {{Mathematical and physical concerns regarding cryptographic key length}}, school = {Catholic University of Louvain, Louvain-la-Neuve, Belgium}, year = {2009}, url = {https://dblp.org/rec/phd/basesearch/Bulens09}, classes = {ECDLP 0.5, Factoring/FF-DLP 0.5}, category = {D}, rationale = {Thesis on key-length models with hardware ECDLP attack cost data point.}, vetted = {yes}, peerreviewed = {no}, quantum = {no}, sources = {dblp, openalex_phrase}, studyid = {dblp:phd/basesearch/Bulens09}, countyear = {2009}, venuenote = {published venue resolved from dblp phd/basesearch/Bulens09 (confidence 1.00)} } @inproceedings{openalex:W2157026519, author = {R. Padmavathy and Chakravarthy Bhagvati}, title = {{Methods to Solve Discrete Logarithm Problem for Ephemeral Keys}}, booktitle = {2009 International Conference on Advances in Recent Technologies in Communication and Computing}, year = {2009}, doi = {10.1109/artcom.2009.62}, url = {https://doi.org/10.1109/artcom.2009.62}, classes = {Factoring/FF-DLP 1}, category = {A}, rationale = {Index-calculus variant for prime-field DLP with smooth p-1.}, vetted = {no}, peerreviewed = {yes}, quantum = {no}, sources = {openalex_phrase}, studyid = {W2157026519}, countyear = {2009}, venuenote = {published venue resolved from crossref 10.1109/artcom.2009.62 (confidence 0.95)} } @inproceedings{dblp:conf-dagstuhl-BuchmannDMM09, author = {Johannes Buchmann and Jintai Ding and Mohamed Saied Emam Mohamed and Wael Said Abd Elmageed Mohamed}, title = {{MutantXL: Solving Multivariate Polynomial Equations for Cryptanalysis}}, booktitle = {Symmetric Cryptography}, howpublished = {Dagstuhl Seminar Proceedings}, year = {2009}, doi = {10.4230/dagsemproc.09031.10}, url = {https://doi.org/10.4230/dagsemproc.09031.10}, classes = {Multivariate 1}, category = {A}, rationale = {MutantXL polynomial system solver benchmarked on HFE versus F4.}, vetted = {yes}, peerreviewed = {no}, quantum = {no}, sources = {dblp, openalex_phrase}, studyid = {dblp:conf/dagstuhl/BuchmannDMM09}, countyear = {2009}, venuenote = {published venue resolved from dblp conf/dagstuhl/BuchmannDMM09 (confidence 1.00)} } @article{openalex:W2121115867, author = {Subhamoy Maitra and Y. V. Subba Rao and Pantelimon Stănică and Sugata Gangopadhyay}, title = {{Nontrivial Solutions to the Cubic Sieve Congruence Problem}}, journal = {Computación y Sistemas}, year = {2009}, doi = {10.13053/cys-12-3-1202}, url = {https://doi.org/10.13053/cys-12-3-1202}, classes = {}, category = {A}, rationale = {Solving cubic sieve congruences for index calculus; weak prime classes.}, vetted = {no}, peerreviewed = {yes}, quantum = {no}, version = {same work as openalex:W2116805499; counted there, weight 0 here}, sources = {openalex_phrase}, studyid = {W2121115867}, countyear = {2009}, venuenote = {published venue resolved from dblp journals/cys/MaitraRSG09 [+dblp-title,openalex] (confidence 0.98)} } @article{openalex:W2116805499, author = {Subhamoy Maitra and Y. V. Subba Rao and Pantelimon Stănică and Sugata Gangopadhyay}, title = {{Nontrivial Solutions to the Cubic Sieve Congruence Problem: x³ = y²z mod p}}, journal = {Computación y Sistemas}, year = {2009}, url = {https://openalex.org/W2116805499}, classes = {Factoring/FF-DLP 1}, category = {A}, rationale = {Finding cubic sieve congruence solutions for index-calculus DLP; weak prime classes.}, vetted = {no}, peerreviewed = {yes}, quantum = {no}, sources = {openalex_phrase}, studyid = {W2116805499}, countyear = {2009}, venuenote = {published venue resolved from dblp journals/cys/MaitraRSG09 (retitled? sim 0.916: Nontrivial Solutions to the Cubic Sieve Congruence Problem) [+dblp-fuzzy,openalex] (confidence 0.88)} } @misc{openalex:W2587096130, author = {김진수}, title = {{NTRU에 대한 Splitting system을 이용한 Hybrid 공격 : A Hybrid Attack Using Splitting Systems Against NTRU}}, year = {2009}, url = {https://openalex.org/W2587096130}, classes = {Lattices 1}, category = {A}, rationale = {Hybrid attack on NTRU using splitting systems.}, vetted = {no}, peerreviewed = {no}, quantum = {no}, sources = {openalex_phrase}, studyid = {W2587096130}, countyear = {2009} } @phdthesis{zbmath:1358.11002, author = {Diem, Claus}, title = {{On arithmetic and the discrete logarithm problem in class groups of curves}}, school = {Habilitation thesis (Claus Diem, 2009)}, year = {2009}, url = {https://zbmath.org/?q=an:1358.11002}, classes = {ECDLP 1}, category = {A}, rationale = {Diem's work on index calculus DLP in class groups of curves; title only.}, vetted = {no}, peerreviewed = {no}, quantum = {no}, sources = {zbmath}, studyid = {zb:1358.11002}, countyear = {2009}, venuenote = {published venue resolved from duplicate-check agent (zbMATH, web-checked): habilitation; MoC 2011 article derived from it (confidence 0.80)} } @article{openalex:W2331303371, author = {Gerhard Frey}, title = {{On Bilinear Structures on Divisor Class Groups}}, journal = {Annales mathématiques Blaise Pascal}, year = {2009}, doi = {10.5802/ambp.250}, url = {https://doi.org/10.5802/ambp.250}, classes = {ECDLP 0.6, Factoring/FF-DLP 0.4}, category = {C}, rationale = {Pairing-based transfer of curve DLP to Brauer groups; structural reduction theory.}, vetted = {no}, peerreviewed = {yes}, quantum = {no}, sources = {openalex_phrase}, studyid = {W2331303371}, countyear = {2009}, venuenote = {published venue resolved from crossref 10.5802/ambp.250 [+crossref,openalex] (confidence 0.98)} } @misc{eprint:2009-058, author = {Takakazu Satoh}, title = {{On Generalization of Cheon's Algorithm}}, howpublished = {Cryptology {ePrint} Archive, Paper 2009/058}, eprint = {2009/058}, eprinttype = {iacr}, eprintclass = {Public-key cryptography}, year = {2009}, url = {https://eprint.iacr.org/2009/058}, classes = {ECDLP 0.5, Factoring/FF-DLP 0.5}, category = {A}, rationale = {Generalization of Cheon's strong Diffie-Hellman algorithm to higher-degree divisors.}, vetted = {yes}, peerreviewed = {no}, quantum = {no}, sources = {eprint}, studyid = {2009/058}, countyear = {2009} } @incollection{dblp:series-ciss-LubiczS09, author = {David Lubicz and Thomas Sirvent}, title = {{On Generic Groups and Related Bilinear Problems}}, booktitle = {Cryptology and Information Security Series}, year = {2009}, doi = {10.3233/978-1-58603-947-9-169}, url = {https://doi.org/10.3233/978-1-58603-947-9-169}, classes = {ECDLP 0.6, Factoring/FF-DLP 0.4}, category = {F}, rationale = {Generic group model analysis of bilinear DL-related problems.}, vetted = {yes}, peerreviewed = {no}, quantum = {no}, sources = {dblp, openalex}, studyid = {dblp:series/ciss/LubiczS09}, countyear = {2009}, venuenote = {published venue resolved from crossref 10.3233/978-1-58603-947-9-169 (confidence 0.95)} } @inproceedings{dblp:conf-asiacrypt-JagerS09, author = {Tibor Jager and Jörg Schwenk}, title = {{On the Analysis of Cryptographic Assumptions in the Generic Ring Model}}, booktitle = {ASIACRYPT 2009}, year = {2009}, doi = {10.1007/978-3-642-10366-7_24}, url = {https://doi.org/10.1007/978-3-642-10366-7_24}, classes = {Factoring/FF-DLP 1}, category = {F}, rationale = {Generic ring model limits: Jacobi symbol equivalent to factoring generically.}, vetted = {yes}, peerreviewed = {yes}, quantum = {no}, sources = {dblp, eprint, openalex}, studyid = {dblp:conf/asiacrypt/JagerS09}, countyear = {2009}, venuenote = {published venue resolved from dblp conf/asiacrypt/JagerS09 [+crossref,dblp-self] (confidence 1.00)} } @article{zbmath:1552.11147, author = {Babul', O. V.}, title = {{On the construction of a system of linear equations in the number field sieve algorithm for solving the discrete logarithm problem}}, journal = {Vestsi Natsyyanal'naĭ Akadèmii Navuk Belarusi. Seryya Fizika-Matèmatychnykh Navuk}, year = {2009}, url = {https://zbmath.org/?q=an:1552.11147}, classes = {Factoring/FF-DLP 1}, category = {A}, rationale = {Title only: linear-system construction step of NFS for finite-field DLP.}, vetted = {no}, peerreviewed = {yes}, quantum = {no}, sources = {zbmath}, studyid = {zb:1552.11147}, countyear = {2009}, venuenote = {published venue resolved from zbmath 1552.11147 (confidence 0.90)} } @misc{eprint:2009-389, author = {Joppe W. Bos and Marcelo E. Kaihara and Thorsten Kleinjung and Arjen K. Lenstra and Peter L. Montgomery}, title = {{On the Security of 1024-bit RSA and 160-bit Elliptic Curve Cryptography}}, howpublished = {Cryptology {ePrint} Archive, Paper 2009/389}, eprint = {2009/389}, eprinttype = {iacr}, eprintclass = {Public-key cryptography}, year = {2009}, url = {https://eprint.iacr.org/2009/389}, classes = {ECDLP 0.5, Factoring/FF-DLP 0.5}, category = {D}, rationale = {Risk assessment of 1024-bit RSA and 160-bit ECC from record computation data.}, vetted = {yes}, peerreviewed = {no}, quantum = {no}, sources = {eprint}, studyid = {2009/389}, countyear = {2009} } @misc{eprint:2009-483, author = {Jean-Charles Faugère and Ludovic Perret}, title = {{On the Security of UOV}}, howpublished = {Cryptology {ePrint} Archive, Paper 2009/483}, eprint = {2009/483}, eprinttype = {iacr}, eprintclass = {Public-key cryptography}, year = {2009}, url = {https://eprint.iacr.org/2009/483}, classes = {Multivariate 1}, category = {A}, rationale = {Hybrid Groebner basis forgery attack on UOV parameters.}, vetted = {yes}, peerreviewed = {no}, quantum = {no}, sources = {eprint}, studyid = {2009/483}, countyear = {2009} } @inproceedings{dblp:conf-europar-BackesW09, author = {Werner Backes and Susanne Wetzel}, title = {{Parallel Lattice Basis Reduction Using a Multi-threaded Schnorr-Euchner LLL Algorithm}}, booktitle = {Euro-Par}, year = {2009}, doi = {10.1007/978-3-642-03869-3_88}, url = {https://doi.org/10.1007/978-3-642-03869-3_88}, classes = {Lattices 1}, category = {A}, rationale = {Parallel Schnorr-Euchner LLL; v0.3.4 counts faster LLL variants.}, vetted = {yes}, peerreviewed = {yes}, quantum = {no}, sources = {dblp, openalex_snowball}, studyid = {dblp:conf/europar/BackesW09}, countyear = {2009}, venuenote = {published venue resolved from dblp conf/europar/BackesW09 (confidence 1.00)} } @inproceedings{eprint:2009-601, author = {Jens Hermans and Michael Schneider and Johannes Buchmann and Frederik Vercauteren and Bart Preneel}, title = {{Parallel Shortest Lattice Vector Enumeration on Graphics Cards}}, eprint = {2009/601}, eprinttype = {iacr}, eprintclass = {Implementation}, booktitle = {AFRICACRYPT 2010}, note = {Also Cryptology {ePrint} Archive, Paper 2009/601}, year = {2010}, doi = {10.1007/978-3-642-12678-9_4}, url = {https://eprint.iacr.org/2009/601}, classes = {Lattices 1}, category = {A}, rationale = {Parallel GPU lattice enumeration for SVP with large speedups.}, vetted = {yes}, peerreviewed = {yes}, quantum = {no}, sources = {eprint}, studyid = {2009/601}, countyear = {2009}, venuenote = {published venue resolved from dblp conf/africacrypt/HermansSBVP10 (confidence 0.95)} } @article{zbmath:1207.94062, author = {Sarkar, Santanu and Maitra, Subhamoy}, title = {{Partial key exposure attacks on RSA and its variant by guessing a few bits of one of the prime factors}}, journal = {Bulletin of the Korean Mathematical Society}, year = {2009}, doi = {10.4134/bkms.2009.46.4.721}, url = {https://doi.org/10.4134/bkms.2009.46.4.721}, classes = {}, category = {C}, rationale = {Lattice partial key exposure attacks on RSA and Sun-Yang variant.}, vetted = {no}, peerreviewed = {yes}, quantum = {no}, sources = {zbmath}, studyid = {zb:1207.94062}, countyear = {2009}, venuenote = {published venue resolved from crossref 10.4134/bkms.2009.46.4.721 [+crossref,zbmath] (confidence 0.98)} } @article{openalex:W2082241842, author = {R. Padmavathy and Chakravarthy Bhagvati}, title = {{Performance analysis of index calculus method}}, journal = {Journal of Discrete Mathematical Sciences and Cryptography}, year = {2009}, doi = {10.1080/09720529.2009.10698242}, url = {https://doi.org/10.1080/09720529.2009.10698242}, classes = {Factoring/FF-DLP 1}, category = {A}, rationale = {Improved random and partial linear sieve index calculus for prime-field DLP.}, vetted = {no}, peerreviewed = {yes}, quantum = {no}, sources = {openalex_phrase, zbmath}, studyid = {W2082241842}, countyear = {2009}, venuenote = {published venue resolved from crossref 10.1080/09720529.2009.10698242 [+crossref,openalex] (confidence 0.98)} } @inproceedings{zbmath:1202.65032, author = {Meletiou, Gerasimos C.}, title = {{Polynomial interpolation of the \textbackslash{}(k\textbackslash{})-th root of the discrete logarithm}}, booktitle = {Algebraic Informatics}, year = {2009}, doi = {10.1007/978-3-642-03564-7_21}, url = {https://doi.org/10.1007/978-3-642-03564-7_21}, classes = {Factoring/FF-DLP 1}, category = {F}, rationale = {Polynomial interpolation lower bounds for DL-related function; restricted-model hardness.}, vetted = {no}, peerreviewed = {yes}, quantum = {no}, sources = {zbmath}, studyid = {zb:1202.65032}, countyear = {2009}, venuenote = {published venue resolved from crossref 10.1007/978-3-642-03564-7\_21 (confidence 0.95)} } @misc{eprint:2009-509, author = {Valerie Gauthier Umana and Gregor Leander}, title = {{Practical Key Recovery Attacks On Two McEliece Variants}}, howpublished = {Cryptology {ePrint} Archive, Paper 2009/509}, eprint = {2009/509}, eprinttype = {iacr}, eprintclass = {Public-key cryptography}, year = {2009}, url = {https://eprint.iacr.org/2009/509}, classes = {Syndrome decoding 1}, category = {C}, rationale = {Structural key recovery on quasi-cyclic and quasi-dyadic McEliece variants.}, vetted = {yes}, peerreviewed = {no}, quantum = {no}, sources = {eprint}, studyid = {2009/509}, countyear = {2009} } @incollection{dblp:series-isc-ValleeV10, author = {Brigitte Vallée and Antonio Vera}, title = {{Probabilistic Analyses of Lattice Reduction Algorithms}}, booktitle = {The LLL Algorithm}, year = {2009}, doi = {10.1007/978-3-642-02295-1_3}, url = {https://doi.org/10.1007/978-3-642-02295-1_3}, classes = {Lattices 1}, category = {A}, rationale = {Probabilistic analysis of LLL/Gauss reduction; v0.3.4 counts average-case reduction analyses.}, vetted = {yes}, peerreviewed = {no}, quantum = {no}, sources = {dblp, openalex_snowball, zbmath}, studyid = {dblp:series/isc/ValleeV10}, countyear = {2009}, venuenote = {published venue resolved from dblp series/isc/ValleeV10 [+crossref,dblp-self] (confidence 1.00)} } @inproceedings{dblp:conf-dagstuhl-Schneider09, author = {Michael Schneider}, title = {{Probabilistic Analysis of LLL Reduced Bases}}, booktitle = {Algorithms and Number Theory}, howpublished = {Dagstuhl Seminar Proceedings}, year = {2009}, doi = {10.4230/dagsemproc.09221.4}, url = {https://doi.org/10.4230/dagsemproc.09221.4}, classes = {Lattices 1}, category = {A}, rationale = {Probabilistic analysis of LLL output quality; average-case reduction analysis.}, vetted = {yes}, peerreviewed = {no}, quantum = {no}, sources = {dblp, openalex_snowball}, studyid = {dblp:conf/dagstuhl/Schneider09}, countyear = {2009}, venuenote = {published venue resolved from dblp conf/dagstuhl/Schneider09 (confidence 1.00)} } @article{dblp:journals-corr-abs-0912-4807, author = {Arthur Schmidt}, title = {{Quantum Algorithms for many-to-one Functions to Solve the Regulator and the Principal Ideal Problem}}, journal = {CoRR}, howpublished = {arXiv}, year = {2009}, doi = {10.48550/arxiv.0912.4807}, url = {https://doi.org/10.48550/arxiv.0912.4807}, classes = {Lattices 1}, category = {B}, rationale = {Quantum algorithms for regulator and principal ideal problem; PIP underlies ideal-lattice attacks.}, vetted = {yes}, peerreviewed = {no}, quantum = {yes}, sources = {dblp}, studyid = {dblp:journals/corr/abs-0912-4807}, countyear = {2009}, venuenote = {published venue resolved from dblp journals/corr/abs-0912-4807 (confidence 1.00)} } @inproceedings{dblp:conf-csie-ZhouLWD09, author = {Haijian Zhou and Ping Luo and Daoshun Wang and Yiqi Dai}, title = {{Remarks on Cryptanalysis of RSA Using Lattice Basis Reduction}}, booktitle = {2009 WRI World Congress on Computer Science and Information Engineering}, year = {2009}, doi = {10.1109/csie.2009.890}, url = {https://doi.org/10.1109/csie.2009.890}, classes = {}, category = {A}, rationale = {Title only: remarks on lattice-reduction cryptanalysis of RSA.}, vetted = {yes}, peerreviewed = {yes}, quantum = {no}, sources = {dblp}, studyid = {dblp:conf/csie/ZhouLWD09}, countyear = {2009}, venuenote = {published venue resolved from crossref 10.1109/csie.2009.890 (confidence 0.95)} } @article{openalex:W2058748538, author = {Haijian Zhou and Ping Luo and Daoshun Wang and Yiqi Dai}, title = {{Remarks on the bounds for cryptanalysis of low private key RSA}}, journal = {Progress in Natural Science}, year = {2009}, doi = {10.1016/j.pnsc.2008.09.013}, url = {https://doi.org/10.1016/j.pnsc.2008.09.013}, classes = {}, category = {H}, rationale = {Disputes Boneh-Durfee d