LEADER 01011nam0-22003251i-450- 001 990004564210403321 005 20140331125933.0 035 $a000456421 035 $aFED01000456421 035 $a(Aleph)000456421FED01 035 $a000456421 100 $a19990604g19461845km-y0itay50------ba 101 0 $aspa 105 $ay-------001yy 200 1 $aDiego Lainez en la Europa religiosa de su tiempo$e1512-1565$fpor Feliciano Cereceda 210 $aMadrid$cEdiciones Cultura Hispanica$d1945-1946 215 $a2 v.$d23 cm 610 0 $aGesuiti spagnoli 610 0 $aLaínez, Diego S.F.,--1512-1565. 676 $a271.53024 676 $a922.246 700 1$aCereceda,$bFeliciano$f<1901-1950>$0494673 801 0$aIT$bUNINA$gRICA$2UNIMARC 901 $aBK 912 $a990004564210403321 952 $a271.53 CER 1 (1)$bBibl. 22773a$fFLFBC 952 $a271.53 CER 1 (2)$bBibl. 22773b$fFLFBC 959 $aFLFBC 996 $aDiego Lainez en la Europa religiosa de su tiempo$9549142 997 $aUNINA LEADER 00892nam0-22003131i-450- 001 990000450590403321 005 20070725125808.0 010 $a0-85038-769-8 035 $a000045059 035 $aFED01000045059 035 $a(Aleph)000045059FED01 035 $a000045059 100 $a20020821d1984----km-y0itay50------ba 101 0 $aeng 105 $aa-------001yy 200 1 $aIndustrial robot specifications$fCompilated by André Cugy, Kogan Page 210 $aLondon$cKogan Page$dc1984 215 $a357 p.$cill.$d30 cm 610 0 $aRobot - Industriali$aAutomazione 676 $a629.892 700 1$aCugy,$bAndre$025150 701 1$aPage,$bAndré$0347020 801 0$aIT$bUNINA$gRICA$2UNIMARC 901 $aBK 912 $a990000450590403321 952 $a10 D III 400$b228 DIS$fDINEL 959 $aDINEL 996 $aIndustrial robot specifications$9334096 997 $aUNINA LEADER 05112nam 22004693 450 001 9910860804003321 005 20230823200926.0 010 $a1-62705-537-1 035 $a(CKB)4330000000043111 035 $a(MiAaPQ)EBC6955508 035 $a(Au-PeEL)EBL6955508 035 $a(OCoLC)958512196 035 $a(EXLCZ)994330000000043111 100 $a20230823d2015 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aCandidate Multilinear Maps 205 $a1st ed. 210 1$aSan Rafael :$cMorgan & Claypool Publishers,$d2015. 210 4$d©2015. 215 $a1 online resource (125 pages) 225 1 $aACM Bks. 327 $aIntro -- Contents -- Preface -- 1. Introduction -- Our Results -- Brief Overview -- Organization -- 2. Survey of Applications -- How Flexible Can We Make Access to Encrypted Data? -- Program Obfuscation -- Other Applications -- 3. Multilinear Maps and Graded Encoding Systems -- Cryptographic Multilinear Maps -- Graded Encoding Schemes -- 4. Preliminaries I: Lattices -- Lattices -- Gaussians on Lattices -- Sampling from Discrete Gaussian -- 5. Preliminaries II: Algebraic Number Theory Background -- Number Fields and Rings of Integers -- Embeddings and Geometry -- Ideals in the Ring of Integers -- Prime Ideals-Unique Factorization and Distributions -- Ideal Lattices -- 6. The New EncodingSchemes -- The Basic Graded Encoding Scheme -- Setting the Parameters -- Extensions and Variants -- 7. Security of OurConstructions -- Our Hardness Assumption -- Simplistic Models of Attacks -- Cryptanalysis Beyond the Generic Models -- Some Countermeasures -- Easiness of Other Problems -- 8. Preliminaries III: Computation in a Number Field -- Some Computational Aspects of Number Fields and Ideal Lattices -- Computational Hardness Assumptions over Number Fields -- 9. Survey of LatticeCryptanalysis -- Averaging Attacks -- Gentry-Szydlo: Recovering v from v . v and v -- Nguyen-Regev: A Gradient Descent Attack -- Ducas-Nguyen: Gradient Descent over Zonotopes and Deformed Parallelepipeds -- A New Algorithm for the Closest Principal Ideal Generator Problem -- Coppersmith Attacks -- Dimension Halving in Principal Ideal Lattices -- 10 One-Round Key Exchange -- Definitions -- Our Construction -- A. Generalizing Graded Encoding Systems -- Efficient Procedures-The Dream Version -- Efficient Procedures-The Real-Life Version -- Hardness Assumptions -- Bibliography -- Author's Biography. 330 $aCryptography to me is the "black magic," of cryptographers, enabling tasks that often seem paradoxical or simply just impossible. Like the space explorers, we cryptographers often wonder, "what are the boundaries of this world of black magic?" This work lays one of the founding stones in furthering our understanding of these edges. We describe plausible lattice-based constructions with properties that approximate the sought after multilinear maps in hard-discrete-logarithm groups. The security of our constructions relies on seemingly hard problems in ideal lattices, which can be viewed as extensions of the assumed hardness of the NTRU function. These new constructions radically enhance our tool set and open a floodgate of applications. We present a survey of these applications. This book is based on my PhD thesis which was an extended version of a paper titled "Candidate Multilinear Maps from Ideal Lattices" co-authored with Craig Gentry and Shai Halevi. This paper was originally published at EUROCRYPT 2013. The aim of cryptography is to design primitives and protocols that withstand adversarial behavior. Information theoretic cryptography, how-so-ever desirable, is extremely restrictive and most non-trivial cryptographic tasks are known to be information theoretically impossible. In order to realize sophisticated cryptographic primitives, we forgo information theoretic security and assume limitations on what can be efficiently computed. In other words we attempt to build secure systems conditioned on some computational intractability assumption such as factoring, discrete log, decisional Diffie-Hellman, learning with errors, and many more. In this work, based on the 2013 ACM Doctoral Dissertation Award-winning thesis, we put forth new plausible lattice-based constructions with properties that approximate the sought after multilinear maps. The 330 8 $amultilinear analog of the decision Diffie-Hellman problem appears to be hard in our construction, and this allows for their use in cryptography. These constructions open doors to providing solutions to a number of important open problems. 410 0$aACM Bks. 606 $aCryptography 606 $aData encryption (Computer science) 615 0$aCryptography. 615 0$aData encryption (Computer science). 676 $a005.8 700 $aGarg$b Sanjam$01741747 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910860804003321 996 $aCandidate Multilinear Maps$94167963 997 $aUNINA