Search

Your search keyword '"Player Rachel"' showing total 4 results
Start Over Author "Player Rachel" Search Limiters Full Text
4 results on '"Player Rachel"'

1. Discretisation and Product Distributions in Ring-LWE

Author

Murphy Sean and Player Rachel

Subjects
ring-lwe, discretisation, homomorphic encryption, 94a60, 11t71, Mathematics, QA1-939
Abstract

A statistical framework applicable to Ring-LWE was outlined by Murphy and Player (IACR eprint 2019/452). Its applicability was demonstrated with an analysis of the decryption failure probability for degree-1 and degree-2 ciphertexts in the homomorphic encryption scheme of Lyubashevsky, Peikert and Regev (IACR eprint 2013/293). In this paper, we clarify and extend results presented by Murphy and Player. Firstly, we make precise the approximation of the discretisation of a Normal random variable as a Normal random variable, as used in the encryption process of Lyubashevsky, Peikert and Regev. Secondly, we show how to extend the analysis given by Murphy and Player to degree-k ciphertexts, by precisely characterising the distribution of the noise in these ciphertexts.

Published
2020
Full Text
View/download PDF

2. On the concrete hardness of Learning with Errors

Author

Albrecht Martin R., Player Rachel, and Scott Sam

Subjects
learning with errors, lattice-based cryptography, lattice reduction, 94a60, 11t71, Mathematics, QA1-939
Abstract

The learning with errors (LWE) problem has become a central building block of modern cryptographic constructions. This work collects and presents hardness results for concrete instances of LWE. In particular, we discuss algorithms proposed in the literature and give the expected resources required to run them. We consider both generic instances of LWE as well as small secret variants. Since for several methods of solving LWE we require a lattice reduction step, we also review lattice reduction algorithms and use a refined model for estimating their running times. We also give concrete estimates for various families of LWE instances, provide a Sage module for computing these estimates and highlight gaps in the knowledge about algorithms for solving the LWE problem.

Published
2015
Full Text
View/download PDF

3. Parameter selection in lattice-based cryptography

Author

Player, Rachel

Subjects
005.8, Lattice-based cryptography, Homomorphic encryption, Learning with errors
Abstract

Public-key cryptography in use today is based on classically hard problems such as factoring or solving discrete logarithms. These problems could be efficiently solved if an adversary had access to a sufficiently large quantum computer. The potential of such a quantum computer therefore represents a threat on current cryptography. The field of post-quantum cryptography aims to mitigate against this threat by proposing schemes based on alternative assumptions that are believed to be hard in both the classical and quantum setting. Lattice-based cryptography has emerged as a promising candidate for post-quantum cryptography. One reason for this is the wealth of applications that are possible, perhaps the most notable of which is Fully Homomorphic Encryption (FHE). This enables computations to be performed on encrypted data, without requiring access to the secret key, and for these computations to correspond to operations on the underlying data in a meaningful way. The Learning with Errors (LWE) problem and its variants, such as LWE with small secret, LWE with binary error, and Ring-LWE, are used as hardness assumptions in many lattice-based schemes. In this thesis we consider parameter selection in cryptosystems based on LWE. We begin with a focus on security by considering the concrete hardness of LWE. We comprehensively review the algorithms that can be used to solve LWE and its variants with a small secret. Turning our attention to an LWE variant where the error distribution is binary, we show there is an additional attack applicable in this setting. In applications, the selection of appropriate parameters is often very challenging due to the conflicting requirements of security, correctness and performance. We highlight this in the application setting of FHE by considering a scheme based on Ring-LWE. In particular, we discuss the selection of parameters in SEAL, an implementation of the scheme by Fan and Vercauteren.

Published
2018

4. Discretisation and Product Distributions in Ring-LWE.

Author

Murphy, Sean and Player, Rachel

Subjects
RANDOM variables, FAILURE analysis
Abstract

A statistical framework applicable to Ring-LWE was outlined by Murphy and Player (IACR eprint 2019/452). Its applicability was demonstrated with an analysis of the decryption failure probability for degree-1 and degree-2 ciphertexts in the homomorphic encryption scheme of Lyubashevsky, Peikert and Regev (IACR eprint 2013/293). In this paper, we clarify and extend results presented by Murphy and Player. Firstly, we make precise the approximation of the discretisation of a Normal random variable as a Normal random variable, as used in the encryption process of Lyubashevsky, Peikert and Regev. Secondly, we show how to extend the analysis given by Murphy and Player to degree-k ciphertexts, by precisely characterising the distribution of the noise in these ciphertexts. [ABSTRACT FROM AUTHOR]

Published
2021
Full Text
View/download PDF

Catalog

Books, media, physical & digital resources
See catalog results