Known-Plaintext Attack to Two Cryptosystems Based on the BB Equation

Known-Plaintext Attack to Two Cryptosystems Based on the BB Equation

Recently, Rama Murthy and Swamy proposed a symmetric cryptosystem based on the Brahmagupta-Bhaskara (BB) equation. The BB equation is the quadratic Diophantine equation nx 2 + k = y 2 , where k is an integer and n is a positive integer such that radic( n) is irrational. For the particular case k =1,...

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Bibliographic Details
Published in:IEEE transactions on circuits and systems. II, Express briefs Vol. 55; no. 5; pp. 423 - 426
Main Authors: Alvarez, G., Encinas, L.H., Masque, J.M.
Format: Journal Article
Language:English
Published: New York IEEE 01-05-2008
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Brahmagupta-BhÃskara (BB) equation
Circuits
cryptanalysis
Cryptography
Diophantine equation
Equations
Galois fields
Hardware
Information processing
Integers
Linear systems
Mathematical analysis
Pell equation
Physics
Security
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Summary:Recently, Rama Murthy and Swamy proposed a symmetric cryptosystem based on the Brahmagupta-Bhaskara (BB) equation. The BB equation is the quadratic Diophantine equation nx 2 + k = y 2 , where k is an integer and n is a positive integer such that radic( n) is irrational. For the particular case k =1, the equation is called the Pell equation. The proposed cryptosystem was modified later by the same authors in order to avoid the cryptanalysis given by Youssef. Below, a known-plaintext attack to both cryptosystems is presented.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:1549-7747
1558-3791
DOI:10.1109/TCSII.2007.914441