Duke University Law School Addition, Durham, North Carolina, 1988-1995

[Conceptual Sketches of Elevation and Cupola], untitled. Blue ink sketches on tracing paper, 12 x 20 1/2 inches [from photographic copy by Lance Burgharrdt]

Duke University Law School Addition, Durham, North Carolina, 1988-1995

[Conceptual Sketches of Cupola], untitled. Ink sketches with gray marker coloring on tracing paper, initialed, 19 1/4 x 18 inches [from photographic copy by Lance Burgharrdt]

Duke University Law School Addition, Durham, North Carolina, 1988-1995

[Conceptual Sketches of Cupola], untitled. Ink sketches with gray marker coloring on tracing paper, 15 3/4 x 18 inches [from photographic copy by Lance Burgharrdt]

Duke University Law School Addition, Durham, North Carolina, 1988-1995

[Conceptual Sketches of Cupola], untitled. Ink sketches with gray and green marker coloring on tracing paper, initialed, 17x12 inches [from photographic copy by Lance Burgharrdt]

Duke University Law School Addition, Durham, North Carolina, 1988-1995

[Conceptual Sketches of Cupola], untitled. Ink sketches with gray marker coloring on tracing paper, 14x12 inches [from photographic copy by Lance Burgharrdt]

Ohio State University College of Law Building Addition, Columbus, Ohio 1988-1993

[Early Conceptual Sketch], untitled. Digital image only of black ink sketch on graph paper, initialed

Ohio State University College of Law Building Addition, Columbus, Ohio 1988-1993

[Early Conceptual Sketch], untitled. Digital image only of black ink sketch on graph paper, initialed

Ohio State University College of Law Building Addition, Columbus, Ohio 1988-1993

[Schematic Design Drawing of Site Plan], untitled. Digital image only of black and green ink drawing on blue-line print, initialed

Faster group operations on elliptic curves

This paper improves implementation techniques of Elliptic Curve Cryptography. We introduce new formulae and algorithms for the group law on Jacobi quartic, Jacobi intersection, Edwards, and Hessian curves. The proposed formulae and algorithms can save time in suitable point representations. To support our claims, a cost comparison is made with classic scalar multiplication algorithms using previous and current operation counts. Most notably, the best speeds are obtained from Jacobi quartic curves which provide the fastest timings for most scalar multiplication strategies benefiting from the proposed 12M + 5S + 1D point doubling and 7M + 3S + 1D point addition algorithms. Furthermore, the new addition algorithm provides an efficient way to protect against side channel attacks which are based on simple power analysis (SPA). Keywords: Efficient elliptic curve arithmetic,unified addition, side channel attack.

FPGA montgomery modular multiplication architectures suitable for ECCs over GF(p)

New FPGA architectures for the ordinary Montgomery multiplication algorithm and the FIOS modular multiplication algorithm are presented. The embedded 18×18-bit multipliers and fast carry look-ahead logic located on the Xilinx Virtex2 Pro family of FPGAs are used to perform the ordinary multiplications and additions/subtractions required by these two algorithms. The architectures are developed for use in Elliptic Curve Cryptosystems over GF(p), which require modular field multiplication to perform elliptic curve point addition and doubling. Field sizes of 128-bits and 256-bits are chosen but other field sizes can easily be accommodated, by rapidly reprogramming the FPGA. Overall, the larger the word size of the multiplier, the more efficiently it performs in terms of area/time product. Also, the FIOS algorithm is flexible in that one can tailor the multiplier architecture is to be area efficient, time efficient or a mixture of both by choosing a particular word size. It is estimated that the computation of a 256-bit scalar point multiplication over GF(p) would take about 4.8 ms.