Cryptography and Lattices: International Conference, CaLC 2001, Providence, RI, USA, March 29-30, 2001. Revised Papers

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Joseph H. Silverman
Springer Science & Business Media, Aug 15, 2001 - Computers - 217 pages
ThesearetheproceedingsofCaLC2001, the?rstconferencedevotedtocr- tographyandlattices. Wehavelongbelievedthattheimportanceoflattices andlatticereductionincryptography, bothforcryptographicconstructionand cryptographicanalysis, meritsagatheringdevotedtothistopic. Theenthusiastic responsethatwereceivedfromtheprogramcommittee, theinvitedspeakers, the manypeoplewhosubmittedpapers, andthe90registeredparticipantsamply con?rmedthewidespreadinterestinlatticesandtheircryptographicappli- tions. WethankeveryonewhoseinvolvementmadeCaLCsuchasuccessfulevent; inparticularwethankNatalieJohnson, LarryLarrivee, DoreenPappas, andthe BrownUniversityMathematicsDepartmentfortheirassistanceandsupport. March2001 Je?reyHo?stein, JillPipher, JosephSilverman VI Preface Organization CaLC2001wasorganizedbytheDepartmentofMathematicsatBrownUniv- sity. Theprogramchairsexpresstheirthankstotheprogramcommiteeandthe additionalexternalrefereesfortheirhelpinselectingthepapersforCaLC2001. TheprogramchairswouldalsoliketothankNTRUCryptosystemsforproviding nancialsupportfortheconference. Program Commitee DonCoppersmith IBMResearch Je?reyHo?stein(co-chair), BrownUniversityandNTRUCryptosystems ArjenLenstra Citibank, USA PhongNguyen ENS AndrewOdlyzko AT&TLabsResearch JosephH. Silverman(co-chair), BrownUniversityandNTRUCryptosystems External Referees AliAkhavi, GlennDurfee, NickHowgrave-Graham, DanieleMicciancio Sponsoring Institutions NTRUCryptosystems, Inc., Burlington, MA Table of Contents An Overveiw of the Sieve Algorithm forthe Shortest Lattice Vector Problem 1 Miklos Ajtai, Ravi Kumar, and Dandapani Sivakumar Low Secret Exponent RSA Revisited::::::::::::::::::::::::::::::::: 4 Johannes Bl] omer and Alexander May Finding Small Solutions to Small Degree Polynomials::::::::::::::::::: 20 Don Coppersmith Fast Reduction of Ternary Quadratic Forms::::::::::::::::::::::::::: 32 Friedrich Eisenbrand and Gunt ] er Rote Factoring Polynomialsand 0-1 Vectors:::::::::::::::::::::::::::::::: 45 Mark van Hoeij Approximate Integer Common Divisors::::::::::::::::::::::::::::::: 51 Nick Howgrave-Graham Segment LLL-Reduction of Lattice Bases::::::::::::::::::::::::::::: 67 Henrik Koy and Claus Peter Schnorr Segment LLL-Reduction with Floating Point Orthogonalization:::::::::: 81 Henrik Koy and Claus Peter Schnorr TheInsecurity ofNyberg-Rueppel andOther DSA-LikeSignatureSchemes with Partially Known Nonces:::::::::::::::::::::::::::::::::::::::: 97 Edwin El Mahassni, Phong Q. Nguyen, and Igor E. Shparlinski Dimension Reduction Methods for Convolution Modular Lattices:::::::: 110 Alexander May and Joseph H. Silverman Improving Lattice Based Cryptosystems Using the Hermite Normal Form: 126 Daniele Micciancio The Two Faces of Lattices in Cryptology:::::::::::::::::::::::::::::: 146 Phong Q.
 

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Contents

An Overview of the Sieve Algorithm for the Shortest Lattice Vector Problem
1
Low Secret Exponent RSA Revisited
4
Finding Small Solutions to Small Degree Polynomials
20
Fast Reduction of Ternary Quadratic Forms
32
Approximate Integer Common Divisors
51
Segment LLLReduction of Lattice Bases
67
Segment LLLReduction with Floating Point Orthogonalization
81
The Insecurity of NybergRueppel and Other DSALike Signature Schemes with Partially Known Nonces
97
Dimension Reduction Methods for Convolution Modular Lattices
110
Improving Lattice Based Cryptosystems Using the Hermite Normal Form
126
The Two Faces of Lattices in Cryptology
146
A 3Dimensional Lattice Reduction Algorithm
181
The Shortest Vector Problem in Lattices with Many Cycles
194
Multisequence Synthesis over an Integral Domain
206
Author Index
218
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