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We present a bit-parallel squarer for GF(2n) defined by an irreducible trinomial xn +xk +1 using a shifted polynomial basis. The proposed squarer requires TX delay and at most n/2 XOR gates, where TX is the delay of one XOR gate. As a result, the squarer using the shifted polynomial basis is more efficient than one using the polynomial basis except for k=1 or n/2.