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Three Novel Theorems for Applied Cryptography

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International Journal of Computer Applications
© 2013 by IJCA Journal
Volume 74 - Number 13
Year of Publication: 2013
Authors:
Rahul Yadav
Deepak Chaudhary
10.5120/12948-0090

Rahul Yadav and Deepak Chaudhary. Article: Three Novel Theorems for Applied Cryptography. International Journal of Computer Applications 74(13):31-37, July 2013. Full text available. BibTeX

@article{key:article,
	author = {Rahul Yadav and Deepak Chaudhary},
	title = {Article: Three Novel Theorems for Applied Cryptography},
	journal = {International Journal of Computer Applications},
	year = {2013},
	volume = {74},
	number = {13},
	pages = {31-37},
	month = {July},
	note = {Full text available}
}

Abstract

With advancements in computing capabilities public key cryptosystems are going to be more complex yet vulnerable over the modern day's computer networks and associated security mechanism, especially those based on novel approaches of applied mathematics. This paper explores three novel theorems derived while studying and implementing RSA algorithm, one of the strongest public key cryptosystem. The proposed Theorems are best suited and adequate for RSA algorithm yet being applicable to some of other existing algorithms and theorems of applied mathematics. The first theorem deals with concept of ambiguity while calculating multiplicative inverse of encryption key which in some of instances returns undesirable negative numbers not useful as decryption key . Second theorem deals with unconcealed multiplicative inverses, unconcealed are values which remain unchanged after any mathematical transformations. Concept of unconcealed multiplicative inverses is useful in key generation for RSA cryptosystem. Third theorem deals with the concept of unconcealed exponentiation modulo quite useful in finding unconcealed signature and messages to form UM Matrix for RSA.

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