On Ideal Lattices and Learning with Errors over Rings

2010 ◽  
pp. 1-23 ◽  
Author(s):  
Vadim Lyubashevsky ◽  
Chris Peikert ◽  
Oded Regev
Keyword(s):  
Ideal Lattices ◽  
Learning With Errors

On Ideal Lattices and Learning with Errors over Rings

2013 ◽  
Vol 60 (6) ◽  
pp. 1-35 ◽  
Author(s):  
Vadim Lyubashevsky ◽  
Chris Peikert ◽  
Oded Regev
Keyword(s):  
Ideal Lattices ◽  
Learning With Errors

scholarly journals Mildly Short Vectors in Cyclotomic Ideal Lattices in Quantum Polynomial Time

2021 ◽  
Vol 68 (2) ◽  
pp. 1-26
Author(s):  
Ronald Cramer ◽  
Léo Ducas ◽  
Benjamin Wesolowski
Keyword(s):  
Polynomial Time ◽  
Ideal Lattices ◽  
Quantum Polynomial

Ring-Learning with Errors Cryptography

2020 ◽  
pp. 343-357
Author(s):  
Marius Iulian Mihailescu ◽  
Stefania Loredana Nita
Keyword(s):  
Learning With Errors

Middle-Product Learning with Errors

2017 ◽  
pp. 283-297 ◽  
Author(s):  
Miruna Roşca ◽  
Amin Sakzad ◽  
Damien Stehlé ◽  
Ron Steinfeld
Keyword(s):  
Learning With Errors

scholarly journals Counting Bounded Elements of a Number Field

2020 ◽  
Author(s):  
Mikołaj Fraczyk ◽  
Gergely Harcos ◽  
Péter Maga
Keyword(s):  
Group Theory ◽  
Number Field ◽  
Geometry Of Numbers ◽  
Combine Group ◽  
Successive Minima ◽  
Ideal Lattices ◽  
Linearly Independent ◽  
Ramification Theory

Abstract We estimate, in a number field, the number of elements and the maximal number of linearly independent elements, with prescribed bounds on their valuations. As a by-product, we obtain new bounds for the successive minima of ideal lattices. Our arguments combine group theory, ramification theory, and the geometry of numbers.

Morita invariants of semirings

2015 ◽  
Vol 15 (02) ◽  
pp. 1650023 ◽  
Author(s):  
Sujit Kumar Sardar ◽  
Sugato Gupta
Keyword(s):  
Morita Equivalence ◽  
Ideal Lattices ◽  
Congruence Lattices

In this paper we revisit that ideal lattices and congruence lattices are preserved by Morita equivalence of semirings which is originally obtained implicitly by Katsov and his co-authors. This is then used to obtain some Morita invariants for semirings.

scholarly journals Balancing Access Control and Privacy for Data Deduplication via Functional Encryption

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Bo Mi ◽  
Ping Long ◽  
Yang Liu ◽  
Fengtian Kuang
Keyword(s):  
Access Control ◽  
Security Analysis ◽  
Functional Encryption ◽  
Data Deduplication ◽  
Paper Briefly ◽  
Storage Security ◽  
Redundancy Removal ◽  
Proof Of Ownership ◽  
Learning With Errors ◽  
And Storage

Data deduplication serves as an effective way to optimize the storage occupation and the bandwidth consumption over clouds. As for the security of deduplication mechanism, users’ privacy and accessibility are of utmost concern since data are outsourced. However, the functionality of redundancy removal and the indistinguishability of deduplication labels are naturally incompatible, which bring about a lot of threats on data security. Besides, the access control of sharing copies may lead to infringement on users’ attributes and cumbersome query overheads. To balance the usability with the confidentiality of deduplication labels and securely realize an elaborate access structure, a novel data deduplication scheme is proposed in this paper. Briefly speaking, we drew support from learning with errors (LWE) to make sure that the deduplication labels are only differentiable during the duplication check process. Instead of authority matching, the proof of ownership (PoW) is then implemented under the paradigm of inner production. Since the deduplication label is light-weighted and the inner production is easy to carry out, our scheme is more efficient in terms of computation and storage. Security analysis also indicated that the deduplication labels are distinguishable only for duplication check, and the probability of falsifying a valid ownership is negligible.

MPSign: A Signature from Small-Secret Middle-Product Learning with Errors

2020 ◽  
pp. 66-93
Author(s):  
Shi Bai ◽  
Dipayan Das ◽  
Ryo Hiromasa ◽  
Miruna Rosca ◽  
Amin Sakzad ◽  
...  
Keyword(s):  
Learning With Errors
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