In the implementation of some public key cryptosystems, in particular, the verification procedure of most common digital signatures (apart from RSA) are required to perform not only exponentiation, but also pairs of exponentiation directly. In this paper, a left-to-right adaptive 2-ary window representation (2-AWR) for pairs of integers is presented and analyzed. Shamir algorithm can be on-line carried out using this representation. And its advantage over other similar algorithm is demonstrated.