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by: Americo Huel

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6

# Special Topics in Computer Science and Engineering CSE 5095

Marketplace > University of Connecticut > Engineering Computer Science > CSE 5095 > Special Topics in Computer Science and Engineering
Americo Huel
UCONN
GPA 3.73

Zhijie Shi

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COURSE
PROF.
Zhijie Shi
TYPE
Class Notes
PAGES
6
WORDS
KARMA
25 ?

## Popular in Engineering Computer Science

This 6 page Class Notes was uploaded by Americo Huel on Thursday September 17, 2015. The Class Notes belongs to CSE 5095 at University of Connecticut taught by Zhijie Shi in Fall. Since its upload, it has received 34 views. For similar materials see /class/205924/cse-5095-university-of-connecticut in Engineering Computer Science at University of Connecticut.

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Date Created: 09/17/15
Fast Implementation of Elliptic Curve Cryptosystems Presented by Hal Yan CSE 5095 Fall 2008 0 Introduction 0 Fast ECC implementation over GFp 0 Fast ECC implementation over GF239 0 Conclusion 0 ECC provides similar security strength With shorter key length 0 Elliptic curves defined over GFp or GFZ are used in cryptography 0 Performance of ECC is mainly determined by a Point coordinates 0 Finite field arithmetic I Algorithms for scalar point multiplications Elliptic Curves over GFp y2 X3 aX b Addition of two points X1 i X2 xiv Vi X21 V2 X3 Y3 A 02 39 VlX2 39 X04 X3 x 2 39 Xi 39 X2 Y3 9 X3 39yl Doubling of a point X1 at 0 xii Vi xii Vi st V3 l 3X12 a2yi l X3 XZZX1 Y3 X1X3 Vi J Alternative Coordinates o Projective coordinates PX Y Z oxXZyYZ o Jacobian coordinates PX Y Z a x XZZ y YZ3 o Modified Jacobian coordinates PX Y Z aZ4 a x XZZ y YZ3 Comparison of Cost of Point Addition Af ne Projective Jacobian Medl ed Mixed1 J acoblan Addition I2MS 12MZS 12M4S 13M6S 8M3S Doubling 1 2M ZS 7MSS 4M6S 4M4S NA I Inversion M multiplication S squaring 1 Mixed coordinate is one point in Af ne andthe other in Jacobian coordinate J Finite Field Arithmetic o Addtion and subtraction t c a b mod p o Multiplication c a b mod p o Inversion icalmodpca39lmodp Modular Reduction 0 Pencilandpaper 0 Optimization for special modulo PseudoMersenne prime p 2m a C c lJr O AB C of mod p Multiplication on GFp 0 RowWise multiplication o A an1 a1 a0 B bn1 b1 b0 I Each word has k bits 31 HI n EH gt b Row 0 Row 1 Multiplication o Columnwise multiplication ColZnZ Multiplication con t 0 Hybrid multiplication Gura04 AAmrlA1A0 1303 131139 m4 39 A is divided into m ceilnd groups each groups has dwords 7 d Ali 20 w llyluirl Mulcipiimim ill ll 2 mmLl 1M mmmm 2 11 211 ginVin 2 2 4 in 7 mm a IIl05121ln wt 211 47 2n rm 2n

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