Download or read book Lattice Based Cryptography Security Foundations and Constructions written by Adeline Roux-Langlois and published by . This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lattice-based cryptography is a branch of cryptography exploiting the presumed hardness of some well-known problems on lattices. Its main advantages are its simplicity, efficiency, and apparent security against quantum computers. The principle of the security proofs in lattice-based cryptography is to show that attacking a given scheme is at least as hard as solving a particular problem, as the Learning with Errors problem (LWE) or the Small Integer Solution problem (SIS). Then, by showing that those two problems are at least as hard to solve than a hard problem on lattices, presumed polynomial time intractable, we conclude that the constructed scheme is secure.In this thesis, we improve the foundation of the security proofs and build new cryptographic schemes. We study the hardness of the SIS and LWE problems, and of some of their variants on integer rings of cyclotomic fields and on modules on those rings. We show that there is a classical hardness proof for the LWE problem (Regev's prior reduction was quantum), and that the module variants of SIS and LWE are also hard to solve. We also give two new lattice-based group signature schemes, with security based on SIS and LWE. One is the first lattice-based group signature with logarithmic signature size in the number of users. And the other construction allows another functionality, verifier-local revocation. Finally, we improve the size of some parameters in the work on cryptographic multilinear maps of Garg, Gentry and Halevi in 2013.

Download or read book A Decade of Lattice Cryptography written by Chris Peikert and published by . This book was released on 2016-03-07 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: Surveys most of the major developments in lattice cryptography over the past ten years. The main focus is on the foundational short integer solution (SIS) and learning with errors (LWE) problems, their provable hardness assuming the worst-case intractability of standard lattice problems, and their many cryptographic applications.

Download or read book Lattice Based Cryptography written by Jonathan Katz and published by CRC Press. This book was released on 2018-06-15 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main focus of the book will graduate level courses on the techniques used in obtaining lattice-based cryptosystems. The book will first cover the basics of lattices and then introduce the more advanced material (e.g. Gaussian distributions, sampling, algebraic number theory, etc.) in a "natural" way, motivated by cryptographic constructions. There will also be a fair amount of mathematics that will be introduced gradually and will be motivated by cryptographic constructions.

Download or read book Towards Practical Lattice based Cryptography written by Vadim Lyubashevsky and published by . This book was released on 2008 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lattice-based cryptography began with the seminal work of Ajtai (Ajtai '96) who showed that it is possible to build families of cryptographic functions in which breaking a randomly chosen element of the family is as hard as solving worst-case instances of lattice problems. This work generated great interest and resulted in constructions of many other cryptographic protocols with security based on worst-case lattice problems. An additional advantage of lattice-based primitives is that, unlike their counterparts based on factoring and discrete log, they are conjectured to be secure in the advent of quantum computing. The main disadvantage of lattice-based constructions is that they generally involve operations on, and storage of, large n x n matrices. This resulted in the schemes being rather inefficient and unsuitable for practical use. To cope with this inherent inefficiency, Micciancio proposed to build lattice-based primitives based on the worst-case hardness of lattices that have some additional structure. In (Micciancio '02), he showed how to build one-way functions, computable in almost linear time, with security based on worst-case problems on such lattices. While interesting from a theoretical perspective, one-way functions are not very useful in practice. Our goal in this thesis is to present constructions of practical and efficient cryptographic protocols whose security is based on worst-case hardness of lattice problems. We first show how to build collision-resistant hash functions whose security is based on the hardness of lattice problems in all lattices with a special structure. The special structure that the lattices possess is that they are ideals of certain polynomial rings. The hash functions that we build have almost linear running time, and in practice turn out to be essentially as efficient as ad-hoc constructions that have no provable security. We also give constructions of provably-secure identification and signature schemes whose asymptotic running times are almost linear (up to poly-logarithmic factors), and so these schemes are much more efficient than comparable primitives with security based on factoring and discrete log. Thus our work implies that by considering ideal lattices, it is possible to have the best of both worlds: security based on worst-case problems and optimal efficiency.

Download or read book Lattice Based Cryptosystems written by Jiang Zhang and published by Springer Nature. This book was released on 2020-10-14 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on lattice-based cryptosystems, widely considered to be one of the most promising post-quantum cryptosystems and provides fundamental insights into how to construct provably secure cryptosystems from hard lattice problems. The concept of provable security is used to inform the choice of lattice tool for designing cryptosystems, including public-key encryption, identity-based encryption, attribute-based encryption, key change and digital signatures. Given its depth of coverage, the book especially appeals to graduate students and young researchers who plan to enter this research area.

Download or read book A Course in Cryptography written by Heiko Knospe and published by American Mathematical Soc.. This book was released on 2019-09-27 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a compact course in modern cryptography. The mathematical foundations in algebra, number theory and probability are presented with a focus on their cryptographic applications. The text provides rigorous definitions and follows the provable security approach. The most relevant cryptographic schemes are covered, including block ciphers, stream ciphers, hash functions, message authentication codes, public-key encryption, key establishment, digital signatures and elliptic curves. The current developments in post-quantum cryptography are also explored, with separate chapters on quantum computing, lattice-based and code-based cryptosystems. Many examples, figures and exercises, as well as SageMath (Python) computer code, help the reader to understand the concepts and applications of modern cryptography. A special focus is on algebraic structures, which are used in many cryptographic constructions and also in post-quantum systems. The essential mathematics and the modern approach to cryptography and security prepare the reader for more advanced studies. The text requires only a first-year course in mathematics (calculus and linear algebra) and is also accessible to computer scientists and engineers. This book is suitable as a textbook for undergraduate and graduate courses in cryptography as well as for self-study.

Download or read book Foundations and Practice of Security written by Guy-Vincent Jourdan and published by Springer Nature. This book was released on 2023-03-31 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 15th International Symposium on Foundations and Practice of Security, FPS 2022, held in Ottawa, ON, Canada, during December 12–14, 2022. The 26 regular and 3 short papers presented in this book were carefully reviewed and selected from 83 submissions. The papers have been organized in the following topical sections: Cryptography; Machine Learning; Cybercrime and Privacy; Physical-layer Security; Blockchain; IoT and Security Protocols; and Short Papers.

Download or read book Cryptographic Hardware and Embedded Systems CHES 2012 written by Emmanuel Prouff and published by Springer. This book was released on 2012-09-05 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 14th International Workshop on Cryptographic Hardware and Embedded Systems, CHES 2012, held in Leuven, Belgium, in September 2012. The 32 papers presented together with 1 invited talk were carefully reviewed and selected from 120 submissions. The papers are organized in the following topical sections: intrusive attacks and countermeasures; masking; improved fault attacks and side channel analysis; leakage resiliency and security analysis; physically unclonable functions; efficient implementations; lightweight cryptography; we still love RSA; and hardware implementations.

Download or read book Public Key Cryptography PKC 2018 written by Michel Abdalla and published by Springer. This book was released on 2018-03-05 with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two-volume set LNCS 10769 and 10770 constitutes the refereed proceedings of the 21st IACR International Conference on the Practice and Theory of Public-Key Cryptography, PKC 2018, held in Rio de Janeiro, Brazil, in March 2018. The 49 revised papers presented were carefully reviewed and selected from 186 submissions. They are organized in topical sections such as Key-Dependent-Message and Selective-Opening Security; Searchable and Fully Homomorphic Encryption; Public-Key Encryption; Encryption with Bad Randomness; Subversion Resistance; Cryptanalysis; Composable Security; Oblivious Transfer; Multiparty Computation; Signatures; Structure-Preserving Signatures; Functional Encryption; Foundations; Obfuscation-Based Cryptographic Constructions; Protocols; Blockchain; Zero-Knowledge; Lattices.

Download or read book Lattice Based Public Key Cryptography in Hardware written by Sujoy Sinha Roy and published by Springer Nature. This book was released on 2019-11-12 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the efficient implementation of public-key cryptography (PKC) to address the security challenges of massive amounts of information generated by the vast network of connected devices, ranging from tiny Radio Frequency Identification (RFID) tags to powerful desktop computers. It investigates implementation aspects of post quantum PKC and homomorphic encryption schemes whose security is based on the hardness of the ring-learning with error (LWE) problem. The work includes designing an FPGA-based accelerator to speed up computation on encrypted data in the cloud computer. It also proposes a more practical scheme that uses a special module called recryption box to assist homomorphic function evaluation, roughly 20 times faster than the implementation without this module.

Download or read book An Introduction to Mathematical Cryptography written by Jeffrey Hoffstein and published by Springer. This book was released on 2014-09-11 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required. This text provides an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. The book includes an extensive bibliography and index; supplementary materials are available online. The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include: classical cryptographic constructions, such as Diffie–Hellmann key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem, and digital signatures; fundamental mathematical tools for cryptography, including primality testing, factorization algorithms, probability theory, information theory, and collision algorithms; an in-depth treatment of important cryptographic innovations, such as elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem. The second edition of An Introduction to Mathematical Cryptography includes a significant revision of the material on digital signatures, including an earlier introduction to RSA, Elgamal, and DSA signatures, and new material on lattice-based signatures and rejection sampling. Many sections have been rewritten or expanded for clarity, especially in the chapters on information theory, elliptic curves, and lattices, and the chapter of additional topics has been expanded to include sections on digital cash and homomorphic encryption. Numerous new exercises have been included.

Download or read book Complexity of Lattice Problems written by Daniele Micciancio and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lattices are geometric objects that can be pictorially described as the set of intersection points of an infinite, regular n-dimensional grid. De spite their apparent simplicity, lattices hide a rich combinatorial struc ture, which has attracted the attention of great mathematicians over the last two centuries. Not surprisingly, lattices have found numerous ap plications in mathematics and computer science, ranging from number theory and Diophantine approximation, to combinatorial optimization and cryptography. The study of lattices, specifically from a computational point of view, was marked by two major breakthroughs: the development of the LLL lattice reduction algorithm by Lenstra, Lenstra and Lovasz in the early 80's, and Ajtai's discovery of a connection between the worst-case and average-case hardness of certain lattice problems in the late 90's. The LLL algorithm, despite the relatively poor quality of the solution it gives in the worst case, allowed to devise polynomial time solutions to many classical problems in computer science. These include, solving integer programs in a fixed number of variables, factoring polynomials over the rationals, breaking knapsack based cryptosystems, and finding solutions to many other Diophantine and cryptanalysis problems.

Download or read book The LLL Algorithm written by Phong Q. Nguyen and published by Springer Science & Business Media. This book was released on 2009-12-02 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book to offer a comprehensive view of the LLL algorithm, this text surveys computational aspects of Euclidean lattices and their main applications. It includes many detailed motivations, explanations and examples.

Download or read book Advances in Cryptology ASIACRYPT 2014 written by Palash Sarkar and published by Springer. This book was released on 2014-11-14 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two-volume set LNCS 8873 and 8874 constitutes the refereed proceedings of the 20th International Conference on the Theory and Applications of Cryptology and Information Security, ASIACRYPT 2014, held in Kaoshiung, Taiwan, in December 2014. The 55 revised full papers and two invited talks presented were carefully selected from 255 submissions. They are organized in topical sections on cryptology and coding theory; authenticated encryption; symmetric key cryptanalysis; side channel analysis; hyperelliptic curve cryptography; factoring and discrete log; cryptanalysis; signatures; zero knowledge; encryption schemes; outsourcing and delegation; obfuscation; homomorphic cryptography; secret sharing; block ciphers and passwords; black-box separation; composability; multi-party computation.

Download or read book Attribute based Encryptions and Formal Verification of Lattice based Cryptography written by Xiong Fan and published by . This book was released on 2019 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the early works of Ajtai (STOC'96) and Regev (STOC'05), lattice-based cryptography has proven to be a powerful building block in cryptography. My research focuses on further exploring the expressive power of lattice-based cryptography, as well as formal verification of lattice-based cryptographic schemes. Deniable encryption (Canetti et al. CRYPTO '97) is an intriguing primitive that provides a security guarantee against not only eavesdropping attacks as required by semantic security, but also stronger coercion attacks performed after the fact. The concept of deniability has later demonstrated useful and powerful in many other contexts, such as leakage resilience, adaptive security of protocols, security against selective opening attacks and coercion resistance in voting systems. Despite its conceptual usefulness, our understanding of how to construct deniable primitives under standard assumptions is restricted. We construct a flexibly bi-deniable Attribute-Based Encryption (ABE) scheme for all polynomial-size Branching Programs from Learning With Errors assumption (Regev STOC'05). Attribute based encryption (ABE) is an advanced encryption system with a built-in mechanism to generate keys associated with functions which in turn provide restricted access to encrypted data. Most of the known candidates of attribute based encryption model the functions as circuits. This results in significant efficiency bottlenecks, especially in the setting where the function associated with the ABE key admits a RAM program whose runtime is sublinear in the length of the attribute. We study the notion of attribute based encryption for random access machines (RAMs), introduced in the work of Goldwasser, Kalai, Popa, Vaikuntanathan and Zeldovich (Crypto 2013) and present a construction satisfying sublinear decryption complexity assuming Learning With Errors. We then introduce a symbolic approach for proving security of cryptographic constructions based on the Learning With Errors assumption (Regev, STOC 2005). Such constructions are instances of lattice-based cryptography and are extremely important due to their potential role in post-quantum cryptography. Our approach combines a computational logic, deducibility problems, a standard tool for representing the adversary's knowledge and the Dolev-Yao model. The computational logic is used to capture (indistinguishability-based) security notions and drive the security proofs whereas deducibility problems are used as side-conditions to control that rules of the logic are applied correctly. We then use AutoLWE, an implementation of the logic, to deliver very short or even automatic proofs of several emblematic constructions. The main technical novelty beyond AutoLWE is a set of (semi-)decision procedures for deducibility problems, using extensions of Grobner basis computations for subalgebras in the (non-)commutative setting (instead of ideals in the commutative setting). Our procedures cover the theory of matrices, which is required for lattice-based assumption, as well as the theory of non-commutative rings, fields, and Diffie-Hellman exponentiation, in its standard, bilinear and multilinear forms.

Download or read book Emerging Topics in Hardware Security written by Mark Tehranipoor and published by Springer Nature. This book was released on 2021-04-30 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of emerging topics in the field of hardware security, such as artificial intelligence and quantum computing, and highlights how these technologies can be leveraged to secure hardware and assure electronics supply chains. The authors are experts in emerging technologies, traditional hardware design, and hardware security and trust. Readers will gain a comprehensive understanding of hardware security problems and how to overcome them through an efficient combination of conventional approaches and emerging technologies, enabling them to design secure, reliable, and trustworthy hardware.

Download or read book Information Security Practice and Experience written by Chunhua Su and published by Springer. This book was released on 2018-09-17 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 14th International Conference on Information Security Practice and Experience, ISPEC 2018, held in Tokyo, Japan, in September 2018. The 39 papers presented in this volume were carefully reviewed and selected from 73 submissions. They were organized in topical sections named: system security; public key cryptography; searchable and functional encryption; post-quantum signature schemas; security protocols; network security; authentication; side-channel attacks; security for cyber-physical systems; security in mobile environment; secure computation and data privacy; and cryptographic protocols.