在有些公钥密码体制的实现中，特别是大多数数字签名（除了RSA）的验证过程，不仅需要指数运算，还需要能直接计算指数对。本文研究分析了整数对的从左到右的2阶自适应窗口表示（2-AWR），使用该表示可以使得Shamir算法实时实现，并且在同类算法中具有明显的速度优势。

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.