Book ChapterDOI
NTRU: A Ring-Based Public Key Cryptosystem
Jeffrey Hoffstein,Jill Pipher,Joseph H. Silverman +2 more
- pp 267-288
TLDR
NTRU encryption and decryption use a mixing system suggested by polynomial algebra combined with a clustering principle based on elementary probability theory to create a new public key cryptosystem.Abstract:
We describe NTRU, a new public key cryptosystem. NTRU features reasonably short, easily created keys, high speed, and low memory requirements. NTRU encryption and decryption use a mixing system suggested by polynomial algebra combined with a clustering principle based on elementary probability theory. The security of the NTRU cryptosystem comes from the interaction of the polynomial mixing system with the independence of reduction modulo two relatively prime integers p and q.read more
Citations
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Proceedings ArticleDOI
Fully homomorphic encryption using ideal lattices
TL;DR: This work proposes a fully homomorphic encryption scheme that allows one to evaluate circuits over encrypted data without being able to decrypt, and describes a public key encryption scheme using ideal lattices that is almost bootstrappable.
A fully homomorphic encryption scheme
Dan Boneh,Craig Gentry +1 more
TL;DR: This work designs a somewhat homomorphic "boostrappable" encryption scheme that works when the function f is the scheme's own decryption function, and shows how, through recursive self-embedding, bootstrappable encryption gives fully homomorphic encryption.
Book ChapterDOI
Security and Privacy Aspects of Low-Cost Radio Frequency Identification Systems
TL;DR: Privacy and security risks and how they apply to the unique setting of low-cost RFID devices are described and several security mech- anisms are proposed and suggested areas for future research are suggested.
Proceedings ArticleDOI
Efficient Fully Homomorphic Encryption from (Standard) LWE
TL;DR: In this article, a fully homomorphic encryption scheme based solely on the (standard) learning with errors (LWE) assumption is presented. But the security of their scheme is based on the worst-case hardness of ''short vector problems'' on arbitrary lattices.
Book ChapterDOI
Fully homomorphic encryption from ring-LWE and security for key dependent messages
TL;DR: A somewhat homomorphic encryption scheme that is both very simple to describe and analyze, and whose security reduces to the worst-case hardness of problems on ideal lattices using the RLWE assumption, which allows us to completely abstract out the lattice interpretation.
References
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Journal ArticleDOI
New Directions in Cryptography
TL;DR: This paper suggests ways to solve currently open problems in cryptography, and discusses how the theories of communication and computation are beginning to provide the tools to solve cryptographic problems of long standing.
Journal ArticleDOI
A method for obtaining digital signatures and public-key cryptosystems
TL;DR: An encryption method is presented with the novel property that publicly revealing an encryption key does not thereby reveal the corresponding decryption key.
Journal ArticleDOI
Factoring Polynomials with Rational Coefficients
TL;DR: This paper presents a polynomial-time algorithm to solve the following problem: given a non-zeroPolynomial fe Q(X) in one variable with rational coefficients, find the decomposition of f into irreducible factors in Q (X).
Factoring polynomials with rational coeficients
TL;DR: In this paper, a polynomial-time algorithm was proposed to decompose a primitive polynomials into irreducible factors in Z(X) if the greatest common divisor of its coefficients is 1.
Journal ArticleDOI
Lattice basis reduction: improved practical algorithms and solving subset sum problems
Claus-Peter Schnorr,M. Euchner +1 more
TL;DR: Empirical tests show that the strongest of these algorithms solves almost all subset sum problems with up to 66 random weights of arbitrary bit length within at most a few hours on a UNISYS 6000/70 or within a couple of minutes on a SPARC1 + computer.