Book ChapterDOI
Graph-Induced Multilinear Maps from Lattices
Craig Gentry,Sergey Gorbunov,Shai Halevi +2 more
- pp 498-527
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TLDR
In this article, a graph-induced multilinear encoding scheme from lattices was proposed, in which the arithmetic operations that are allowed are restricted through an explicitly defined directed graph (somewhat similar to the asymmetric variant of previous schemes).Abstract:
Graded multilinear encodings have found extensive applications in cryptography ranging from non-interactive key exchange protocols, to broadcast and attribute-based encryption, and even to software obfuscation. Despite seemingly unlimited applicability, essentially only two candidate constructions are known (GGH and CLT). In this work, we describe a new graph-induced multilinear encoding scheme from lattices. In a graph-induced multilinear encoding scheme the arithmetic operations that are allowed are restricted through an explicitly defined directed graph (somewhat similar to the “asymmetric variant” of previous schemes). Our construction encodes Learning With Errors (LWE) samples in short square matrices of higher dimensions. Addition and multiplication of the encodings corresponds naturally to addition and multiplication of the LWE secrets. Security of the new scheme is not known to follow from LWE hardness (or any other “nice” assumption), at present it requires making new hardness assumptions.read more
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A Decade of Lattice Cryptography.
TL;DR: Lattice-based cryptography is the use of conjectured hard problems on point lattices in Rn as the foundation for secure cryptographic systems as mentioned in this paper, which is the main feature of lattice cryptography.
Posted Content
On the concrete hardness of Learning with Errors.
TL;DR: In this article, the authors present hardness results for concrete instances of LWE and give concrete estimates for various families of instances, provide a Sage module for computing these estimates and highlight gaps in the knowledge about algorithms for solving the Learning with Errors problem.
Book
A Decade of Lattice Cryptography
TL;DR: Lattice-based cryptography is the use of conjectured hard problems on point lattices in Rn as the foundation for secure cryptographic systems as discussed by the authors, which is the main feature of lattice cryptography.
Book ChapterDOI
Cryptanalysis of the New CLT Multilinear Map over the Integers
TL;DR: Two polynomial attacks on the CLT15 multilinear map are presented, which share ideas similar to the cryptanalysis of CLT13 and allow recovery of all secret parameters in timePolynomial in the security parameter, and lead to a full break of theCLT15 multi-million-dollar map for virtually all applications.
Book ChapterDOI
Cryptanalysis of GGH Map
Yupu Hu,Huiwen Jia +1 more
TL;DR: In this paper, the authors present several efficient attacks on GGH map, aiming at multipartite key exchange MKE and the instance of witness encryption WE based on the hardness of exact-3-cover X3C problem.
References
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Journal ArticleDOI
Identity-Based Encryption from the Weil Pairing
Dan Boneh,Matthew K. Franklin +1 more
TL;DR: This work proposes a fully functional identity-based encryption (IBE) scheme based on bilinear maps between groups and gives precise definitions for secure IBE schemes and gives several applications for such systems.
Proceedings ArticleDOI
Attribute-based encryption for fine-grained access control of encrypted data
TL;DR: This work develops a new cryptosystem for fine-grained sharing of encrypted data that is compatible with Hierarchical Identity-Based Encryption (HIBE), and demonstrates the applicability of the construction to sharing of audit-log information and broadcast encryption.
Journal ArticleDOI
Universal classes of hash functions
TL;DR: An input independent average linear time algorithm for storage and retrieval on keys that makes a random choice of hash function from a suitable class of hash functions.
Book ChapterDOI
Efficient identity-based encryption without random oracles
TL;DR: This work first presents their IBE construction and reduces the security of the scheme to the decisional Bilinear Diffie-Hellman (BDH) problem, and shows that their techniques can be used to build a new signature scheme that is secure under the computational Diffie -Hellman assumption without random oracles.
Journal ArticleDOI
A Pseudorandom Generator from any One-way Function
TL;DR: It is shown how to construct a pseudorandom generator from any one-way function, and it is shown that there is a Pseudorandom Generator if and only ifthere is a one- way function.