The following dissertation was written by Benjamin Nickolls from University of Liverpool. Written permission has been given to me to post it here. Thanks to Benjamin Nickolls. - Herong

Attacks on Encryption Schemes

Benjamin Nickolls

Student No. 200133878

May 2005

Supervised by Dr Paul Sant

Honours project submitted to the Department of Computer Science for BCS degree in (BSc) Computer Science.

Ownership of this report remains with the University of Liverpool.

Acknowledgements

I would like to acknowledge the support of Dr. Paul Sant throughout the course of this study. His help and occasional prodding kept the project moving in the face of all adversity.

I would also like to acknowledge the contribution made by Dr. Herong Yang. Approval for the use of his copy written code enabled the implementation of the Reduced-Block DES algorithm possible.

Abstract

In today's world of electronic communication secure transmission of data is a necessity. This dissertation offers a critical appreciation of modern day cryptosystems and the security that they can or can not provide. A discussion of cryptography and cryptanalysis provides the basis for a practical demonstration of two cryptanalytic attacks: An implementation of the RSA public key system is used to illustrate an attack developed by Michael Weiner exploiting a class of weak public keys containing information on the corresponding decryption exponent. This technique utilises the continued fraction algorithm operating in O(n) time with respect the the size of the modulus. A sixteen-bit, private key, block cipher similar to that of the DEA is also presented for the demonstration of a known plaintext, Brute- Force attack executing a linear search of the key space operating in exponential time O(2ⁿ) (where n is the bit-length of the key). Evaluation of this software leads to a debate on the implications of future cryptography and of computer security on a broader level.

Keywords: Cryptanalysis, DES, RSA, Weiner Attack, Brute-Force

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