This paper presents a configuration of parallel multipliers for GF(2m) based on canonical bases. The possible parallel multipliers by the proposed configuration are limited to a class of fields GF(2m). However they can be constructed by O(m2) AND-gates and O(m2) EOR-gates with the structural modularity (this is a desirable feature for the hardware implementation), and their operation time is about (log m) T, where m is the dimension of GF(2m) and T is the delay time of an EOR-gate. In order to construct such parallel multipliers, we define two types of polynomials of special form over GF(2), one is called all one polynomial (denoted by AOP) and the other is called equally spaced polynomial (denoted by ESP). Furthermore, we show a necessary and sufficient condition for ESPs to be irreducible over GF(2) and the uniqueness of the irreducible ESPs over GF(2). Finally, we propose the configuration of parallel multipliers for a class of fields GF(2m) based on irreducible AOPs and ESPs over GF(2).