A Limit Theorem in Cryptography.

<p>Cryptography is the study of encryptying and decrypting messages and deciphering encrypted messages when the code is unknown. We consider &#923;_&#960;(&#916;<em>x</em>, &#916;<em>y</em>) which is a count of how many ways a permutation satisfies a certain property. According to Hawkes and O'Connor, the distribution of &#923;_&#960;(&#916;<em>x</em>, &#916;<em>y</em>) tends to a Poisson distribution with parameter &#189; as <em>m</em> &#8594; &#8734; for all &#916;<em>x</em>,&#916;<em>y</em> &#8712; (<b>Z</b>/<em>q</em><b>Z</b>)^<em>m</em> - 0. We give a proof of this theorem using the Stein-Chen method: As <em>q^m</em> approaches infinity, the distribution of &#923;_&#960;(&#916;<em>x</em>, &#916;<em>y</em>) is approximately Poisson with parameter &#189;. Error bounds for this approximation are provided.</p>

Name thesis:degree_name

MS (Master of Science)

Level thesis:degree_level

Thesis - unrestricted

Discipline thesis:degree_discipline

Mathematical Sciences

Year dc:date.issued

2005

Author dc:creator

• Lynch, Kevin

• Cryptography
• Stein-Chen Method
• Poisson Approximation
• Cryptanalysis
• Error Bound
• Coupling Method
• Even Word
• Multiple of Three Word
• Applied Mathematics
• Physical Sciences and Mathematics

Statement dc:rights

• Copyright by the authors.

Repository record dc:identifier

https://dc.etsu.edu/etd/1042

OAI identifier oai:identifier

oai:dc.etsu.edu:etd-2199