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Quadratic Time, Linear Space Algorithms for Gram-Schmidt Orthogonalization and Gaussian Sampling in Structured Lattices
Lattice-based Cryptography Lattice Techniques Gaussian Sampling
2016/1/3
A procedure for sampling lattice vectors is at the heart of many lattice constructions, and the algorithm of Klein (SODA 2000) and Gentry, Peikert, Vaikuntanathan (STOC 2008) is currently the one that...
Ideal Multilinear Maps Based on Ideal Lattices
Ideal multilinear maps ideal lattices multipartite Diffie–Hellman key exchange
2016/1/3
Cryptographic multilinear maps have many applications, such as multipartite key
exchange and software obfuscation. However, the encodings of three current constructions are
“noisy” and their multili...
Strongly Secure Authenticated Key Exchange from Ideal Lattices
cryptographic protocols practical authenticated key exchange
2015/12/31
In this paper, we propose an efficient and practical authenticated key exchange (AKE) protocol from ideal
lattices, which is well-designed and has some similarity to the HMQV protocol. Using the hard...
Cryptanalysis of the multilinear map on the ideal lattices
Multilinear maps graded encoding schemes zeroizing attack
2015/12/30
We improve the zeroizing attack on the multilinear map of Garg, Gentry and Halevi (GGH). Our algorithm can solve the Graded Decisional Diffie-Hellman (GDDH) problem on the GGH scheme when the dimensio...
Re-encryption, functional re-encryption, and multi-hop re-encryption: A framework for achieving obfuscation-based security and instantiations from lattices
re-encryption average-case obfuscation
2015/12/30
In this work we define multiple relaxations to the definition of
correctness in secure obfuscation. While still remaining meaningful, these
relaxations provide ways to obfuscate many primitives in a...
ILTRU: An NTRU-Like Public Key Cryptosystem Over Ideal Lattices
Lattice-based cryptography Ideal lattices ETRU
2015/12/30
In this paper we present a new NTRU-Like public key cryptosystem with security provably based on the worst case hardness of the approximate both Shortest Vector Problem (SVP) and Closest Vector Proble...
An Improved BKW Algorithm for LWE with Applications to Cryptography and Lattices
cryptanalysis lattice techniques public-key cryptography
2015/12/29
In this paper, we study the Learning With Errors problem and its binary variant, where secrets and errors are binary or taken in a small interval. We introduce a new variant of the Blum, Kalai and Was...
Polynomial Time Reduction from Approximate Shortest Vector Problem to Principal Ideal Problem for Lattices in Some Cyclotomic Rings
Cyclotomic Rings Principal Ideal Problem
2015/12/29
Many cryptographic schemes have been established based on the hardness of lattice problems. For the asymptotic efficiency, ideal lattices in the ring of cyclotomic integers are suggested to be used in...
A Hybrid Gaussian Sampler for Lattices over Rings
Lattice-based Cryptography Gaussian Sampling Ideal Lattices
2015/12/29
Gaussian sampling over lattices is a cornerstone of lattice-based cryptography as it allows to build numerous cryptographic primitives. There are two main algorithms performing this task. The first on...
New multilinear maps from ideal lattices
Multilinear maps Ideal lattices Multipartite Diffie-Hellman key exchange
2015/12/24
Recently, Hu and Jia presented an efficient attack on the GGH13 map. They show that
the MPKE and WE based on GGH13 with public tools of encoding are not secure. Currently, an
open problem is to fix ...
TESLA: Tightly-Secure Efficient Signatures from Standard Lattices
signature scheme lattice cryptography tight security
2015/12/24
Generally, lattice-based cryptographic primitives offer good performance and
allow for strong security reductions. However, the most efficient current lattice-based signature
schemes sacrifice (part...
Security Analysis of Cryptosystems Using Short Generators over Ideal Lattices
Short generators Cyclotomic fields Log-unit lattices
2015/12/22
In this paper, we analyze the security of cryptosystems using
short generators over ideal lattices such as candidate multilinear maps
by Garg, Gentry and Halevi and fully homomorphic encryption by S...
Attribute-Based Encryption for a Subclass of Circuits with Bounded Depth from Lattices
Functional Encryption Attribute-Based Encryption
2014/3/12
In this work, we present two Key-Policy Attribute-Based Encryption (ABE) schemes for some subclass of circuits based on the Learning with Error (LWE) assumption. Our constructions are selectively secu...
Creating a Challenge for Ideal Lattices
implementation Lattice-Based Cryptography Ideal Lattices
2013/2/21
Lattice-based cryptography is one of the candidates in the area of post-quantum cryptography. Cryptographic schemes with security reductions to hard lattice problems (like the Shortest Vector Problem ...
Making NTRUEncrypt and NTRUSign as Secure as Standard Worst-Case Problems over Ideal Lattices
public-key cryptography Lattice based cryptography
2013/2/21
NTRUEncrypt, proposed in 1996 by Hoffstein, Pipher and Silverman, is the fastest known lattice-based encryption scheme. Its moderate key-sizes, excellent asymptotic performance and conjectured resista...