3 citations · 11 across the 11 of their papers we have counts for
12 papers
Existence and Construction of a Gröbner Basis for a Polynomial Ideal
Deepak Kapur, Paliath Narendran
This extended abstract gives a construction for lifting a Gröbner basis algorithm for an ideal in a polynomial ring over a commutative ring R under the condition that R also admits…
CryptoSolve: Towards a Tool for the Symbolic Analysis of Cryptographic Algorithms
Dalton Chichester, Wei Du, Raymond Kauffman +8
Recently, interest has been emerging in the application of symbolic techniques to the specification and analysis of cryptosystems. These techniques, when accompanied by suitable pr…
On Problems Dual to Unification: The String-Rewriting Case
Zümrüt Akçam, Kimberly A. Cornell, Daniel S. Hono +2
In this paper, we investigate problems which are dual to the unification problem, namely the Fixed Point (FP) problem, Common Term (CT) problem and the Common Equation (CE) problem…
On Asymmetric Unification for the Theory of XOR with a Homomorphism
Christopher Lynch, Andrew M. Marshall, Catherine Meadows +2
Asymmetric unification, or unification with irreducibility constraints, is a newly developed paradigm that arose out of the automated analysis of cryptographic protocols. However,…
On Problems Dual to Unification
Zümrüt Akçam, Daniel S. Hono, Paliath Narendran
In this paper, we investigate a problem dual to the unification problem, namely the Common Term (CT) problem for string rewriting systems. Our main motivation was in computing fixe…
Asymmetric Unification and Disunification
Veena Ravishankar, Kimberly A. Gero, Paliath Narendran
We compare two kinds of unification problems: Asymmetric Unification and Disunification, which are variants of Equational Unification. Asymmetric Unification is a type of Equationa…
Lynch-Morawska Systems on Strings
Daniel S. Hono, Paliath Narendran, Rafael Veras
We investigate properties of convergent and forward-closed string rewriting systems in the context of the syntactic criteria introduced in \cite{LynchMorawska} by Christopher Lynch…
Notes on Lynch-Morawska Systems
Daniel S. Hono, Namrata Galatage, Kimberly A. Gero +2
In this paper we investigate convergent term rewriting systems that conform to the criteria set out by Christopher Lynch and Barbara Morawska in their seminal paper "Basic Syntacti…
On Unification Modulo One-Sided Distributivity: Algorithms, Variants and Asymmetry
Andrew M Marshall, Catherine Meadows, Paliath Narendran
An algorithm for unification modulo one-sided distributivity is an early result by Tidén and Arnborg. More recently this theory has been of interest in cryptographic protocol analy…
Unification modulo a 2-sorted Equational theory for Cipher-Decipher Block Chaining
Siva Anantharaman, Christopher Bouchard, Paliath Narendran +1
We investigate unification problems related to the Cipher Block Chaining (CBC) mode of encryption. We first model chaining in terms of a simple, convergent, rewrite system over a s…
On the Complexity of the Tiden-Arnborg Algorithm for Unification modulo One-Sided Distributivity
Paliath Narendran, Andrew Marshall, Bibhu Mahapatra
We prove that the Tiden and Arnborg algorithm for equational unification modulo one-sided distributivity is not polynomial time bounded as previously thought. A set of counterexamp…
Unification modulo a partial theory of exponentiation
Deepak Kapur, Andrew Marshall, Paliath Narendran
Modular exponentiation is a common mathematical operation in modern cryptography. This, along with modular multiplication at the base and exponent levels (to different moduli) play…