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Sieving for shortest vectors in ideal lattices: a practical perspective

Joppe W. Bos, Michael Naehrig, Joop Van De Pol
2017 International Journal of Applied Cryptography  
The security of lattice-based schemes relies on the hardness of lattice problems such as the problem of finding short vectors in integral lattices.  ...  Our results shed additional light on the security of schemes which rely on the hardness of computing short vectors in this special setting.  ...  We thank Nigel Smart for his comments on an earlier version of the paper.  ... 
doi:10.1504/ijact.2017.089353 fatcat:b3svl2e45vca5d4lzxtdvd7cj4

Sieving for shortest vectors in ideal lattices: a practical perspective

Joop Van De Pol, Michael Naehrig, Joppe W. Bos
2017 International Journal of Applied Cryptography  
The security of lattice-based schemes relies on the hardness of lattice problems such as the problem of finding short vectors in integral lattices.  ...  Our results shed additional light on the security of schemes which rely on the hardness of computing short vectors in this special setting.  ...  We thank Nigel Smart for his comments on an earlier version of the paper.  ... 
doi:10.1504/ijact.2017.10010312 fatcat:otrnq6p635hq7in7us7dyjqddm

Computing the character table of a finite group

W.R. Unger
2006 Journal of symbolic computation  
We describe an implementation of such an algorithm and report on its performance. The main ingredients of the algorithm are Brauer's theorem, and lattice reduction by LLL.  ...  We report on the performance of the algorithm in computing character tables of various groups, including local subgroups of 3Fi 24 and maximal subgroups of the Monster.  ...  Acknowledgements I would like to thank John Cannon for his enthusiastic support of this project and Eamonn O'Brien for supplying the groups of Fig. 6 .  ... 
doi:10.1016/j.jsc.2006.04.002 fatcat:4yuc72rmivadrov6g6saztjrty

Improved Zero-Knowledge Identification with Lattices [chapter]

Pierre-Louis Cayrel, Richard Lindner, Markus Rückert, Rosemberg Silva
2010 Lecture Notes in Computer Science  
Auslandsstudium in England an der University of Birmingham iii List of Publications [BDL08] J. Buchmann, M. Döring, and R. Lindner. Efficiency improvement for NTRU. In A. Alkassar and J. H.  ...  In practice, the only rings that have been used and suggested for constructing ideal lattices are maximal orders of cyclotomic number fields.  ...  Let R = Z[x]/f (x) be a polynomial ring for some monic polynomial f (x) that is irreducible over Z; common choices include cyclotomic polynomials such as f (x) = x n + 1 for n a power of 2.  ... 
doi:10.1007/978-3-642-16280-0_1 fatcat:qphlhyww45avzim6wyo7bvnira

Physical-Layer Cryptography Through Massive MIMO

Thomas R. Dean, Andrea J. Goldsmith
2017 IEEE Transactions on Information Theory  
Hence, under the widely-held conjecture that standard lattice problems are hard to solve in the worst-case, the proposed encryption scheme has a more robust notion of security than that of the most common  ...  We show that the eavesdropper's decoder for the MIMO system with M-PAM modulation is equivalent to solving standard lattice problems that are conjectured to be of exponential complexity for both classical  ...  ACKNOWLEDGEMENT The authors would like to thank Dan Boneh for his discussions on lattice-based cryptography, Martin Hellman for his comments on a preliminary version of this work, Shlomo Shamai for discussions  ... 
doi:10.1109/tit.2017.2715187 fatcat:meod6hf75rcdhis4swcocijq4e

Lattice-based cryptosystems

Camelia Karimianpour, Université D'Ottawa / University Of Ottawa, Université D'Ottawa / University Of Ottawa
2013
We describe a generalization of the NTRU cryptosystem over rings other than Z after giving a survey of some of the most famous lattice-based cryptosystems, namely, Ajtai-Dwork, GGH and NTRU.  ...  Our generalization, which follows the idea of CTRU and NTRU over Gaussian integers, implies one may extend the NTRU encryption scheme over integral domains up to some constraints.  ...  CTRU cryptosystem as an example of a NTRU-like cryptosystem over a ring which is a polynomial ring over a field.  ... 
doi:10.20381/ruor-12341 fatcat:tv543mgbvrfnxnrev6uwb3gkp4

SWIFFT: A Modest Proposal for FFT Hashing [chapter]

Vadim Lyubashevsky, Daniele Micciancio, Chris Peikert, Alon Rosen
Lecture Notes in Computer Science  
The functions correspond to a simple algebraic expression over a certain polynomial ring, as described in detail in Section 2.1.  ...  from the family (with noticeable probability) is at least as hard as finding short vectors in cyclic/ideal lattices in the worst case.  ...  Then the ring Z[α]/(α n +1) is isomorphic to Z[ζ 2n ], which is the ring of integers of the so-called cyclotomic number field Q(ζ 2n ).  ... 
doi:10.1007/978-3-540-71039-4_4 fatcat:eus73igcsrdndbybesoxoic5wy

Subgroup Cryptosystems [chapter]

Arjen K. Lenstra
Encyclopedia of Cryptography and Security  
For the CDH and DDH problem similar arguments hold. In the special case that R is a finite field F p d and f is irreducible over R of degree e, the ring R[X]/(f ) is isomorphic to F p de .  ...  Schnorr [161] proposed to use only a subgroup of prime order q of Z * p .  ...  Ter vergelijking worden ook krommen over een lichaam van priemorde beschreven.  ... 
doi:10.1007/0-387-23483-7_418 fatcat:gg3uycmc65a6thhy4gtslscxae