Results 1 
6 of
6
Report on Generic Case Complexity
, 2007
"... This article is a short introduction to generic case complexity, which is a recently developed way of measuring the difficulty of a computational problem while ignoring atypical behavior on a small set of inputs. Generic case complexity applies to both recursively solvable and recursively unsolvable ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
(Show Context)
This article is a short introduction to generic case complexity, which is a recently developed way of measuring the difficulty of a computational problem while ignoring atypical behavior on a small set of inputs. Generic case complexity applies to both recursively solvable and recursively unsolvable problems. Contents
On the cryptanalysis of the generalized simultaneous conjugacy search problem and the security of the algebraic eraser
, 2011
"... ar ..."
(Show Context)
New PublicKey Cryptography Using Polynomials over NonCommutative Rings
, 2007
"... In this paper, we propose a new method for designing public key cryptosystems based on general noncommutative rings. The key idea of our proposal is that for a given noncommutative ring, we can define polynomials and take them as the underlying work structure. By doing so, it is easy to implement ..."
Abstract
 Add to MetaCart
In this paper, we propose a new method for designing public key cryptosystems based on general noncommutative rings. The key idea of our proposal is that for a given noncommutative ring, we can define polynomials and take them as the underlying work structure. By doing so, it is easy to implement DiffieHelmanlike key exchange protocol. And consequently, ElGamallike cryptosystems can be derived immediately. Moreover, we show how to extend our method to noncommutative groups (or semigroups).
Polynomial time solutions of computational problems in noncommutativealgebraic cryptography
, 2013
"... By introducing extra shields on Shpilrain and Ushakov’s KoLeelike protocol based on the decomposition problem of group elements we propose two new key exchange schemes and then a number of public key cryptographic protocols. We show that these protocols are free of known attacks. Particularly, if ..."
Abstract
 Add to MetaCart
By introducing extra shields on Shpilrain and Ushakov’s KoLeelike protocol based on the decomposition problem of group elements we propose two new key exchange schemes and then a number of public key cryptographic protocols. We show that these protocols are free of known attacks. Particularly, if the entities taking part in our protocols create their private keys composed by the generators of the Mihailova subgroups of Bn, we show that the safety of our protocols are very highly guarantied by the insolvability of subgroup membership problem of the Mihailova subgroups.
A New Key Agreement Scheme Based on the Triple Decomposition Problem
"... Abstract A new key agreement scheme based on the triple decomposition problem over noncommutative platforms is presented. A realization of the new scheme over braid groups is provided and the strengths of it over earlier systems that rely on similar decomposition problems are discussed. The new sc ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract A new key agreement scheme based on the triple decomposition problem over noncommutative platforms is presented. A realization of the new scheme over braid groups is provided and the strengths of it over earlier systems that rely on similar decomposition problems are discussed. The new scheme improves over the earlier systems over braid groups by countering the linear algebra and length based attacks to the decomposition problem in braid groups.
Signature Scheme Using the Root Extraction Problem on Quaternions
"... The root extraction problem over quaternion rings modulo an RSA integer is defined, and the intractability of the problem is examined. A signature scheme is constructed based on the root extraction problem. It is proven that an adversary can forge a signature on a message if and only if he can extr ..."
Abstract
 Add to MetaCart
The root extraction problem over quaternion rings modulo an RSA integer is defined, and the intractability of the problem is examined. A signature scheme is constructed based on the root extraction problem. It is proven that an adversary can forge a signature on a message if and only if he can extract the roots for some quaternion integers. The performance and other security related issues are also discussed.