Type of Document Master's Thesis Author Briggs, Matthew Edward Author's Email Address email@example.com URN etd-32298-93111 Title An Introduction to the General Number Field Sieve Degree Master of Science Department Mathematics Advisory Committee
Advisor Name Title Brown, Ezra A. Committee Chair Day, Martin V. Committee Member Parry, Charles J. Committee Member Keywords
- Number Field Sieve
- Algebraic Number Theory
Date of Defense 1998-04-17 Availability unrestricted AbstractWith the proliferation of computers into homes and businesses and the
explosive growth rate of the Internet, the ability to conduct secure
electronic communications and transactions has become an issue of
vital concern. One of the most prominent systems for securing
electronic information, known as RSA, relies upon the fact that it is
computationally difficult to factor a ``large'' integer into its
component prime integers. If an efficient algorithm is developed that
can factor any arbitrarily large integer in a ``reasonable'' amount of
time, the security value of the RSA system would be nullified.
The General Number Field Sieve algorithm is the fastest known method
for factoring large integers. Research and development of this
algorithm within the past five years has facilitated factorizations of
integers that were once speculated to require thousands of years of
supercomputer time to accomplish. While this method has many
unexplored features that merit further research, the complexity of the
algorithm prevents almost anyone but an expert from investigating its
behavior. We address this concern by first pulling together much of the
background information necessary to understand the concepts that are
central in the General Number Field Sieve. These concepts are woven
together into a cohesive presentation that details each theory while
clearly describing how a particular theory fits into the algorithm.
Formal proofs from existing literature are recast and illuminated to
clarify their inner-workings and the role they play in the whole
process. We also present a complete, detailed example of a
factorization achieved with the General Number Field Sieve in order to
concretize the concepts that are outlined.
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