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Winter School on Cryptography: Introduction to Lattices - Oded Regev
 
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Winter School on Lattice-Based Cryptography and Applications, which took place at Bar-Ilan University between february 19 - 22. The event's program: http://crypto.biu.ac.il/winterschool2012/ Dept. of Computer Science: http://www.cs.biu.ac.il/ Bar-Ilan University: http://www1.biu.ac.il/indexE.php
Views: 21867 barilanuniversity
Lattices: from geometry to cryptography - Oded Regev
 
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Ruth and Irving Adler Expository Lecture in Mathematics Topic: Lattices: from geometry to cryptography Speaker: Oded Regev Affiliation: New York University Date: November 29, 2017 For more videos, please visit http://video.ias.edu
Chris Peikert: Lattice-Based Cryptography
 
01:19:38
Tutorial at QCrypt 2016, the 6th International Conference on Quantum Cryptography, held in Washington, DC, Sept. 12-16, 2016. Web site: http://2016.qcrypt.net/
Views: 3242 QuICS
CCS 2016 - ΛОλ: Functional Lattice Cryptography
 
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Authors: Eric Crockett (Georgia Institute of Technology) and Chris Peikert (University of Michigan) presented at CCS 2016 - the 23rd ACM Conference on Computer and Communications Security (Hofburg Palace Vienna, Austria / October 24-28, 2016) - organized by SBA Research
Views: 249 CCS 2016
Lattice-Based Cryptography
 
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We will give a survey of recent work on lattice-based cryptography, mainly focusing on the so-called Learning with Errors (LWE) problem. This problem has turned out to be an amazingly versatile basis for cryptographic constructions, with tens of applications, including the recent celebrated work on fully homomorphic encryption. In addition to applications, we will also mention very recent work providing a better understanding of the security of the problem. The talk does not require any prior knowledge in cryptography or in lattices.
Views: 3633 Microsoft Research
Introduction to Lattice Based Cryptography
 
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This short video introduces the concept of a lattice, why they are being considered as the basis for the next generation of public key cryptography, and a short walk through of a specific encryption algorithm. For a very thorough paper designed to be readable for undergraduates I highly recommend https://eprint.iacr.org/2015/938.pdf. *One technical note: At 1:30 I claim that lattices are composed only of integers. This is not true. Some lattices only contain integers, but in general any rational number will do.
Views: 6842 Matthew Dozer
Daniele Micciancio - Lattice-based public-key cryptography
 
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Daniele Micciancio of the University of California, San Diego presented an invited talk on lattice-based public key cryptography at the 2014 PQCrypto summer school in October, 2014. PQCrypto Summer School: https://pqcrypto2014.uwaterloo.ca/summer-school/ Find out more about IQC! Website - https://uwaterloo.ca/institute-for-qu... Facebook - https://www.facebook.com/QuantumIQC Twitter - https://twitter.com/QuantumIQC
COLLOQUIUM: Foundations of Lattice-based Cryptography (November 2017)
 
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Speaker: Divesh Aggarwal, Centre for Quantum Technologies, NUS Abstract: Lattice-based cryptosystems are perhaps the most promising candidates for post-quantum cryptography as they have strong security proofs based on worst-case hardness of computational lattice problems and are efficient to implement due to their parallelizable structure. Attempts to solve lattice problems by quantum algorithms have been made since Shor’s discovery of the quantum factoring algorithm in the mid-1990s, but have so far met with little success if any at all. The main difficulty is that the periodicity finding technique, which is used in Shor’s factoring algorithm and related quantum algorithms, does not seem to be applicable to lattice problems. In this talk, I will survey some of the main developments in lattice cryptography over the last decade or so. The main focus will be on the Learning With Errors (LWE) and the Short Integer Solution (SIS) problems, their ring-based variants, their provable hardness under the intractability assumptions of lattice problems and their cryptographic applications.
Lattice-Based Cryptography
 
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Most modern cryptography, and public-key crypto in particular, is based on mathematical problems that are conjectured to be infeasible (e.g., factoring large integers). Unfortunately, standard public-key techniques are often too inefficient to be employed in many environments; moreover, all commonly used schemes can in principle be broken by quantum computers. This talk will review my recent work on developing new mathematical foundations for cryptography, using geometric objects called lattices. Compared to more conventional proposals, lattice-based schemes offer a host of potential advantages: they are simple and highly parallelizable, they can be proved secure under mild worst-case hardness assumptions, and they remain unbroken by quantum algorithms. Due to the entirely different underlying mathematics, however, realizing even the most basic cryptographic notions has been a major challenge. Surprisingly, I will show that lattice-based schemes are also remarkably flexible and expressive, and that many important cryptographic goals can be achieved --- sometimes even more simply and efficiently than with conventional approaches. Some of our schemes provide interesting twists on old and cherished cryptographic notions, while others introduce entirely new concepts altogether.
Views: 2646 Microsoft Research
Mathematical Ideas in Lattice Based Cryptography - Jill Pipher
 
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2018 Program for Women and Mathematics Topic: Mathematical Ideas in Lattice Based Cryptography Speaker: Jill Pipher Affiliation: Brown University Date: May 21, 2018 For more videos, please visit http://video.ias.edu
CVP and SVP
 
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Views: 970 Jeff Suzuki
Winter School on Cryptography: Proving Hardness of LWE - Oded Regev
 
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Winter School on Lattice-Based Cryptography and Applications, which took place at Bar-Ilan University between february 19 - 22. The event's program: http://crypto.biu.ac.il/winterschool2012/ Dept. of Computer Science: http://www.cs.biu.ac.il/ Bar-Ilan University: http://www1.biu.ac.il/indexE.php
Views: 1940 barilanuniversity
3rd BIU Winter School on Cryptography: Identity-Based Encryption and Variants - Dan Boneh
 
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The 3rd Bar-Ilan Winter School on Cryptography: Bilinear Pairings in Cryptography, which was held between February 4th - 7th, 2013. The event's program: http://crypto.biu.ac.il/winterschool2013/schedule2013.pdf For All 2013 Winter school Lectures: http://www.youtube.com/playlist?list=PLXF_IJaFk-9C4p3b2tK7H9a9axOm3EtjA&feature=mh_lolz Dept. of Computer Science: http://www.cs.biu.ac.il/ Bar-Ilan University: http://www1.biu.ac.il/indexE.php
Views: 6004 barilanuniversity
01 Daniele Micciancio on "Lattice Cryptography: Introduction and Open Questions"
 
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Daniele Micciancio's August 31 presentation on "Lattice Cryptography: Introduction and Open Questions" at the 2015 UCI Mathematics of Cryptography Conference
Steven Galbraith - Challenges for Lattice Cryptography
 
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Title: Challenges for Lattice Cryptography Speaker: Steven Galbraith (University of Auckland) 7th International Conference on Post-Quantum Cryptography PQCrypto 2016 https://pqcrypto2016.jp/program/
Views: 744 PQCrypto 2016
Daniele Micciancio - Lattice-based public-key cryptography #2
 
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Daniele Micciancio of the University of California, San Diego presented an invited talk on lattice-based public key cryptography at the 2014 PQCrypto summer school in October, 2014. This is part 2 of the talk. PQCrypto Summer School: https://pqcrypto2014.uwaterloo.ca/summer-school/ Find out more about IQC! Website - https://uwaterloo.ca/institute-for-qu... Facebook - https://www.facebook.com/QuantumIQC Twitter - https://twitter.com/QuantumIQC
Phong Nguyen - Lattice-Based Cryptography
 
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Title: Lattice-Based Cryptography Speaker: Phong Nguyen (Inria and CNRS/JFLI and the University of Tokyo) 2016 Post-Quantum Cryptography Winter School https://pqcrypto2016.jp/winter/
Views: 1459 PQCrypto 2016
Winter School on Cryptography: Fully Homomorphic Encryption - Craig Gentry
 
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Winter School on Lattice-Based Cryptography and Applications, which took place at Bar-Ilan University between february 19 - 22. The event's program: http://crypto.biu.ac.il/winterschool2012/ Dept. of Computer Science: http://www.cs.biu.ac.il/ Bar-Ilan University: http://www1.biu.ac.il/indexE.php
Views: 2829 barilanuniversity
04 Daniele Micciancio on Foundations of Lattice Based Crypto
 
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Daniele Micciancio's August 13, 2013 lecture at the UCI Workshop on Lattices with Symmetry.
Winter School on Cryptography: Learning With Errors - Chris Peikert
 
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Winter School on Lattice-Based Cryptography and Applications, which took place at Bar-Ilan University between february 19 - 22. The event's program: http://crypto.biu.ac.il/winterschool2012/ Dept. of Computer Science: http://www.cs.biu.ac.il/ Bar-Ilan University: http://www1.biu.ac.il/indexE.php
Views: 7184 barilanuniversity
A Survey on Ring-LWE Cryptography
 
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The Ring Learning-with-Errors problem, proposed by Lyubashevsky, Peikert and Regev in 2010, is a variant of the traditional Learning-with-Errors problem, and is an active research area in lattice based cryptography. It has drawn increased attention due to the important application to constructing homomorphic encryption schemes. The security of RLWE problems relies on the hardness of certain standard problems over ideal lattices. In the first part of the talk, I will review the basics of RLWE problems, the hardness proofs, and major RLWE encryption schemes. Then I will survey different attacks to RLWE, including our new attacks to non-dual RLWE in sub-cyclotomic fields and small error dual RLWE on prime cyclotomic fields. I will end by summarizing the security situation for various RLWE problems. This is joint work with Kristin Lauter and Katherine Stange.
Views: 1852 Microsoft Research
Winter School on Cryptography: Cryptanalysis of GGH and NTRU Signatures - Oded Regev
 
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Winter School on Lattice-Based Cryptography and Applications, which took place at Bar-Ilan University between february 19 - 22. The event's program: http://crypto.biu.ac.il/winterschool2012/ Dept. of Computer Science: http://www.cs.biu.ac.il/ Bar-Ilan University: http://www1.biu.ac.il/indexE.php
Views: 1765 barilanuniversity
Cryptography from Ideal Lattices
 
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Damien Stehlé, École Normale Supérieure de Lyon The Mathematics of Modern Cryptography http://simons.berkeley.edu/talks/damien-stehle-2015-07-07
Views: 1090 Simons Institute
Chris Peikert - Lattice Cryptography for the Internet
 
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Chris Peikert of Georgia Institute of Technology presented a talk titled: Lattice cryptography for the internet at the 2014 PQCrypto conference in October, 2014. Abstract: In recent years, lattice-based cryptography has been recognized for its many attractive properties, such as strong provable security guarantees and apparent resistance to quantum attacks, flexibility for realizing powerful tools like fully homomorphic encryption, and high asymptotic efficiency. Indeed, several works have demonstrated that for basic tasks like encryption and authentication, lattice-based primitives can have performance competitive with (or even surpassing) those based on classical mechanisms like RSA or Diffie-Hellman. However, there still has been relatively little work on developing lattice cryptography for deployment in real-world cryptosystems and protocols. In this work, we take a step toward that goal, by giving efficient and practical lattice-based protocols for key transport, encryption, and authenticated key exchange that are suitable as "drop-in" components for proposed Internet standards and other open protocols. The security of all our proposals is provable based (sometimes in the random-oracle model) on the well-studied "leaning with errors over rings" problem, and hence on the conjectured worst-case hardness of problems on ideal lattices (against quantum algorithms). One of our main technical innovations (which may be of independent interest) is a simple, low-bandwidth reconciliation technique that allows two parties who "approximately agree" on a secret value to reach exact agreement, a setting common to essentially all lattice-bases encryption schemes. Our technique reduces the ciphertext length of prior (already compact) encryption schemes nearly twofold, at essentially no cost. PQCrypto 2014 Book: http://www.springer.com/computer/security+and+cryptology/book/978-3-319-11658-7 Workshop: https://pqcrypto2014.uwaterloo.ca/ Find out more about IQC! Website - https://uwaterloo.ca/institute-for-qu... Facebook - https://www.facebook.com/QuantumIQC Twitter - https://twitter.com/QuantumIQC
Winter School on Cryptography: Trapdoors and Applications - Chris Peikert
 
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Winter School on Lattice-Based Cryptography and Applications, which took place at Bar-Ilan University between february 19 - 22. The event's program: http://crypto.biu.ac.il/winterschool2012/ Dept. of Computer Science: http://www.cs.biu.ac.il/ Bar-Ilan University: http://www1.biu.ac.il/indexE.php
Views: 2475 barilanuniversity
Daniele Micciancio - Cryptography developments
 
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Daniele Micciancio is a professor of computer science at the University of California, San Diego. As a leader in the field of lattice based cryptography and computational complexity, his research has focused heavily on fully homomorphic encryption and its challenges. Micciancio was visiting IQC for PQCrypto 2014, the 6th international conference on post-quantum cryptography (https://pqcrypto2014.uwaterloo.ca/). Find out more about IQC! Website - https://uwaterloo.ca/institute-for-quantum-computing/ Facebook - https://www.facebook.com/QuantumIQC Twitter - https://twitter.com/QuantumIQC Micciancio explains fully homomorphic encryption and how it relates to his group work on latice algorithms.
Historical Talk on Lattice-Based Cryptography
 
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Daniele Micciancio, UC San Diego The Mathematics of Modern Cryptography http://simons.berkeley.edu/talks/daniele-micciancio-2015-07-06
Views: 1928 Simons Institute
Vinod Vaikuntanathan - Lattices and Cryptography:  A Match Made in Heaven
 
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Vinod Vaikuntanathan of the University of Toronto presented a talk titled: Lattices and cryptography: A match made in heaven at the 2014 PQCrypto conference in October, 2014. PQCrypto 2014 Book: http://www.springer.com/computer/security+and+cryptology/book/978-3-319-11658-7 Workshop: https://pqcrypto2014.uwaterloo.ca/ Find out more about IQC! Website - https://uwaterloo.ca/institute-for-qu... Facebook - https://www.facebook.com/QuantumIQC Twitter - https://twitter.com/QuantumIQC
Daniele Micciancio - The use of cryptography
 
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As a professor of computer science and engineering at the University of California, San Diego, Daniele Micciancio knows that the greatest challenge is to get people to use cryptography. End users are starting to notice the importance of security and privacy, and his research in and is a leader in lattice based cryptography and computational complexity will help develop better systems. Micciancio was visiting IQC for PQCrypto 2014, the 6th international conference on post-quantum cryptography (https://pqcrypto2014.uwaterloo.ca/). Find out more about IQC! Website - https://uwaterloo.ca/institute-for-quantum-computing/ Facebook - https://www.facebook.com/QuantumIQC Twitter - https://twitter.com/QuantumIQC Micciancio explains the important challenge of getting everyday computer users to think about cryptography and the security of their data.
Winter School on Cryptography: A History of Lattice-Based Encryption - Vadim Lyubashevsky
 
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Winter School on Lattice-Based Cryptography and Applications, which took place at Bar-Ilan University between february 19 - 22. The event's program: http://crypto.biu.ac.il/winterschool2012/ Dept. of Computer Science: http://www.cs.biu.ac.il/ Bar-Ilan University: http://www1.biu.ac.il/indexE.php
Views: 3684 barilanuniversity
Duality in Lattice Based Cryptography
 
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Invited talk at PKC 2010 by Daniele Micciancio
Views: 782 TheIACR
LLL Example 2
 
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Views: 1617 Jeff Suzuki
An Overview of Lattice Reduction Algorithms
 
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The best generic tool currently known for attacking lattice-based cryptographic primitives is lattice reduction. Lattice reduction is a representation paradigm: it consists in finding a representation (a basis) of a given lattice that provides easier access to intrinsic properties of that lattice. In this talk, I will give an overview of the state of the art in lattice reduction algorithms. I will also describe how lattice reduction may be used to solve standard problems from lattice-based cryptography, namely, the Learning With Errors (LWE) and Small Integer Solution (SIS) problems.
Views: 1080 Microsoft Research
10  Daniele Micciancio on Lattice Algorithms
 
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Daniele Micciancio's August 14, 2013 lecture at the UCI Workshop on Lattices with Symmetry.
11 Oded Regev on "Fast/er/est algorithm for the Shortest Vector Problem"
 
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Oded Regev's September 2 presentation at the 2015 UCI Mathematics of Cryptography Conference
Winter School on Cryptography: Reduction for Sis - Vadim Lyubashevsky
 
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Winter School on Lattice-Based Cryptography and Applications, which took place at Bar-Ilan University between february 19 - 22. The event's program: http://crypto.biu.ac.il/winterschool2012/ Dept. of Computer Science: http://www.cs.biu.ac.il/ Bar-Ilan University: http://www1.biu.ac.il/indexE.php
Views: 3694 barilanuniversity
Winter School on Cryptography: Ideal Lattices and Applications - Vadim Lyubashevsky
 
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Winter School on Lattice-Based Cryptography and Applications, which took place at Bar-Ilan University between february 19 - 22. The event's program: http://crypto.biu.ac.il/winterschool2012/ Dept. of Computer Science: http://www.cs.biu.ac.il/ Bar-Ilan University: http://www1.biu.ac.il/indexE.php
Views: 2826 barilanuniversity
Trapdoors for Lattices: Simpler, Tighter, Faster, Smaller
 
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Crypto 2011 Rump session presentation for Daniele Micciancio and Chris Peikert, talk given by Chris Peikert
Views: 333 TheIACR
Lattice Based Fully Dynamic Multi Key FHE with Short Ciphertexts
 
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Zvika Brakerski and Renen Perlman, Crypto 2016. See http://www.iacr.org/cryptodb/data/paper.php?pubkey=27676
Views: 286 TheIACR
Johannes A. Buchmann - Post-Quantum Cryptography – an overview
 
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Tutorial Talk 4 by Johannes A. Buchmann at 5th International Conference on Quantum Cryptography (QCrypt 2015) in Hitotsubashi Hall, Tokyo, October 2nd, 2015. Download the slides at: http://2015.qcrypt.net/scientific-program/
Views: 3997 QCrypt 2015
Webcast: NTRU - A Secure, High Performance Alternative to RSA or ECC
 
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This webcast, presented by William Whyte (Chief Scientist, Security Innovation) and Chris Conlon (Software Developer, wolfSSL Inc) discusses how the lattice-based NTRU algorithm works, some of its features and benefits, and the process of migrating from RSA to NTRU
Views: 1407 Security Innovation
The Mathematics of Lattices I
 
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Vinod Vaikuntanathan, Massachusetts Institute of Technology Cryptography Boot Camp http://simons.berkeley.edu/talks/vinod-vaikuntanathan-2015-05-18a
Views: 10195 Simons Institute
05 Jeff Hoffstein on NTRU and Lattice-Based Signatures
 
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Jeff Hoffstein's August 13, 2013 lecture at the UCI Workshop on Lattices with Symmetry.
Winter School on Cryptography: Basic Cryptanalysis - Vadim Lyubashevsky
 
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Winter School on Lattice-Based Cryptography and Applications, which took place at Bar-Ilan University between february 19 - 22. The event's program: http://crypto.biu.ac.il/winterschool2012/ Dept. of Computer Science: http://www.cs.biu.ac.il/ Bar-Ilan University: http://www1.biu.ac.il/indexE.php
Views: 2904 barilanuniversity
Lattice Signatures Schemes
 
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Recent work has solidly established lattice-based signatures as a viable replacement for number-theoretic schemes should quantum computing come into fruition. In fact, the current lattice-based schemes have key and signature sizes comparable to RSA while being an order of magnitude faster. The main focus of this talk will be presenting the main ideas behind the latest results in this area. In addition to the high level intuition, I will try to motivate the many employed optimizations, such as having an NTRU-like public key and sampling from a bimodal Gaussian distribution. Most of the talk will be based on the papers "Lattice Signatures without Trapdoors" and "Lattice Signatures and Bimodal Gaussians". The latter is joint work with Leo Ducas, Alain Durmus, and Tancrede Lepoint.
Views: 654 Microsoft Research
Expressive encryption from hard lattice problems
 
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Traditionally, in cryptography, lattices have been used for cryptanalysis, i.e. in breaking cryptosystems. However, since Ajtai's breakthrough result (in 1996) which established surprising connections between average case and worst case hardness of various lattice problems, there has been great interest in constructing cryptosystems from hard lattice problems. We will describe the first Identity Based Encryption system (in which any arbitrary string, usually name or email address, can be one's public key) from lattices in the standard model (independently discovered by Cash, Hofheinz, Kiltz, Peikert) . Next, we will present methods to substantially improve the above IBE construction to make it more space and time efficient. We will also present a new method for 'lattice basis delegation' which allows the construction of more expressive IBE (hierarchical IBE), and compare this new technique with the earlier basis delegation mechanism of CHKP. To conclude, we will discuss future directions in building even more expressive encryption systems from lattices. The material discussed is from joint work with Dan Boneh and Xavier Boyen.
Views: 306 Microsoft Research
15  Vadim Lyubashevsky on Lattice-Based Digital Signatures
 
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Vadim Lyubashevsky's August 15, 2013 lecture at the UCI Workshop on Lattices with Symmetry. Some of the audio has static.
Pseudorandom Knapsacks and the Sample Complexity of LWE Search-to-Decision Reductions
 
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Talk at crypto 2011. Authors: Daniele Micciancio, Petros Mol. See http://www.iacr.org/cryptodb/data/paper.php?pubkey=23590
Views: 247 TheIACR
Hardness of SIS and LWE with Small Parameters
 
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Talk at crypto 2013. Authors: Daniele Micciancio, Chris Peikert
Views: 286 TheIACR