Computer Science > Cryptography and Security
[Submitted on 28 Sep 2003]
Title:New Lattice Based Cryptographic Constructions
View PDFAbstract: We introduce the use of Fourier analysis on lattices as an integral part of a lattice based construction. The tools we develop provide an elegant description of certain Gaussian distributions around lattice points. Our results include two cryptographic constructions which are based on the worst-case hardness of the unique shortest vector problem. The main result is a new public key cryptosystem whose security guarantee is considerably stronger than previous results ($O(n^{1.5})$ instead of $O(n^7)$). This provides the first alternative to Ajtai and Dwork's original 1996 cryptosystem. Our second result is a family of collision resistant hash functions which, apart from improving the security in terms of the unique shortest vector problem, is also the first example of an analysis which is not based on Ajtai's iterative step. Surprisingly, both results are derived from one theorem which presents two indistinguishable distributions on the segment $[0,1)$. It seems that this theorem can have further applications and as an example we mention how it can be used to solve an open problem related to quantum computation.
References & Citations
Bibliographic and Citation Tools
Bibliographic Explorer (What is the Explorer?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)
Code, Data and Media Associated with this Article
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)
Demos
Recommenders and Search Tools
Influence Flower (What are Influence Flowers?)
Connected Papers (What is Connected Papers?)
CORE Recommender (What is CORE?)
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.