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This paper presents a comprehensive study of the computation of square roots over finite extension fields. We propose two novel algorithms for computing square roots over even field extensions of the form , with , an odd prime and . Both algorithms have an associate computational cost roughly equivalent to one exponentiation in . The first algorithm...
We present a hardware-oriented architecture able to compute a 256-bit prime finite field multiplication efficiently. Taking advantage of the Karatsuba algorithm, the proposed architecture splits a 256-bit integer multiplication into fourteen 64-bit sub-products plus a number of additions that are performed using parallel and pipelined arrangements. The resulting 512-bit partial product is reduced...
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