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.