In this contributions, we propose a new MSB(most significant bit) algorithm based on AOP(All One Polynomial) and two parallel semi-systolic architectures to computes $AB^2$over finite field $GF(2^m)$. The proposed architectures are based on standard basis and use the property of irreducible AOP(All One Polynomial) which is all coefficients of 1. The proposed parallel semi-systolic architecture(PSM) has the critical path of $D_{AND2^+}D_{XOR2}$ per cell and the latency of m+1. The modified parallel semi-systolic architecture(WPSM) has the critical path of $D_{XOR2}$ per cell and has the same latency with PSM. The proposed two architectures, PSM and MPSM, have a low latency and a small hardware complexity compared to the previous architectures. They can be used as a basic architecture for exponentiation, division, and inversion. Since the proposed architectures have regularity, modularity and concurrency, they are suitable for VLSI implementation. They can be used as a basic architecture for algorithms, such as the Diffie-Hellman key exchange scheme, the Digital Signature Algorithm(DSA), and the ElGamal encryption scheme which are needed exponentiation operation. The application of the algorithms can be used cryptosystem implementation based on elliptic curve.