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A d r a c S W e extend the binary algorithm invented by J. for s > r > 0. It is well-known that Euclid's algorithm can be Stein and propose two iterative division algorithms in finite extended to modular division over G F e ) by using variables uand v field GF(2W). AlgorithmEBg exhibits faster convergence while that follow the recurrence of r and s. Stein's binary algorithm is algorithm EBd has reduced complexityin each iteration. A based on the following observations: (1) If r is even and s is odd, (semi-)systolic array is designed for AlgorithBBd, resulting in then gc&d =gc&B,s).(2) If both r a n d s are odd, then gc&s) an area-time complexity better than the best result known to = gca( Ir-4 / 2, mh(r,J3). We can extend Stein's binary (gca3 date based on the extended Euclldalgorithm.

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