Positive Applications of Lattices to Cryptography

نویسنده

  • Cynthia Dwork
چکیده

We describe constructions of several cryptographic primitives, including hash functions, public key cryptosystems, pseudo-random bit generators, and digital signatures, whose security depends on the assumed worst-case or average-case hardness of problems involving lattices.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The Two Faces of Lattices in CryptologyPhong

Lattices are regular arrangements of points in n-dimensional space, whose study appeared in the 19th century in both number theory and crystallography. Since the appearance of the celebrated Lenstra-Lenstra-Lovv asz lattice basis reduction algorithm twenty years ago, lattices have had surprising applications in cryptology. Until recently, the applications of lattices to cryptology were only neg...

متن کامل

A New Ring-Based SPHF and PAKE Protocol On Ideal Lattices

emph{ Smooth Projective Hash Functions } ( SPHFs ) as a specific pattern of zero knowledge proof system are fundamental tools to build many efficient cryptographic schemes and protocols. As an application of SPHFs, emph { Password - Based Authenticated Key Exchange } ( PAKE ) protocol is well-studied area in the last few years. In 2009, Katz and Vaikuntanathan described the first lattice-based ...

متن کامل

History of Lattices in Cryptography

Lattices have been used in mathematics going back at least to the 18th century. However, computational aspects of lattices were not investigated much until the early 1980s, when they were successfully employed for breaking several proposed cryptosystems (among many other applications). It was not until the late 1990s that lattices were first used in the design of cryptographic schemes, and the ...

متن کامل

A characterization of multiwavelet packets on general lattices

The objective of this paper is to establish a complete characterization of multiwavelet packets associated with matrix dilation on general lattices $Gamma$ in $mathbb R^d$ by virtue of time-frequency analysis, matrix theory and operator theory.

متن کامل

EEH: AGGH-like public key cryptosystem over the eisenstein integers using polynomial representations

GGH class of public-key cryptosystems relies on computational problems based on the closest vector problem (CVP) in lattices for their security. The subject of lattice based cryptography is very active and there have recently been new ideas that revolutionized the field. We present EEH, a GGH-Like public key cryptosystem based on the Eisenstein integers Z [ζ3] where ζ3 is a primitive...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1997