Title page for ETD etd-050405-143155

Document Type	thesis
Author Name	Ozturk, Erdinc
URN	etd-050405-143155
Title	Low Power Elliptic Curve Cryptography
Degree	MS
Department	Electrical & Computer Engineering
Advisors	Berk Sunar, Advisor David Cyganski, Committee Member Brian King, Committee Member
Keywords	low power montgomery multiplication Elliptic Curve Crytography modulus scaling unified architecture inversion redundant signed digit
Date of Presentation/Defense	2005-05-05
Availability	unrestricted
Abstract This M.S. thesis introduces new modulus scaling techniques for transforming a class of primes into special forms which enable efficient arithmetic. The scaling technique may be used to improve multiplication and inversion in finite fields. We present an efficient inversion algorithm that utilizes the structure of a scaled modulus. Our inversion algorithm exhibits superior performance to the Euclidean algorithm and lends itself to efficient hardware implementation due to its simplicity. Using the scaled modulus technique and our specialized inversion algorithm we develop an elliptic curve processor architecture. The resulting architecture successfully utilizes redundant representation of elements in GF(p) and provides a low-power, high speed, and small footprint specialized elliptic curve implementation. We also introduce a unified Montgomery multiplier architecture working on the extension fields GF(p), GF(2) and GF(3). With the increasing research activity for identity based encryption schemes, there has been an increasing need for arithmetic operations in field GF(3). Since we based our research on low-power and small footprint applications, we designed a unified architecture rather than having a seperate hardware for GF{3}. To the best of our knowledge, this is the first time a unified architecture was built working on three different extension fields.
Files	thesis_last.pdf

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