In general, there are three popular basis representations, standard （canonical, polynomial） basis, normal basis, and dual basis, for representing elements in GF（2^m）. Various basis representations have their disti...In general, there are three popular basis representations, standard （canonical, polynomial） basis, normal basis, and dual basis, for representing elements in GF（2^m）. Various basis representations have their distinct advantages and have their different associated multiplication architectures. In this paper, we will present a unified systolic multiplication architecture, by employing Hankel matrix-vector multiplication, for various basis representations. For various element representation in GF（2^m）, we will show that various basis multiplications can be performed by Hankel matrix-vector multiplications. A comparison with existing and similar structures has shown that time complexities. the proposed architectures perform well both in space and展开更多
Recently, cryptographic applications based on finite fields have attracted much attention. The most demanding finite field arithmetic operation is multiplication. This investigation proposes a new multiplication algor...Recently, cryptographic applications based on finite fields have attracted much attention. The most demanding finite field arithmetic operation is multiplication. This investigation proposes a new multiplication algorithm over GF（2^m） using the dual basis representation. Based on the proposed algorithm, a parallel-in parallel-out systolic multiplier is presented, The architecture is optimized in order to minimize the silicon covered area （transistor count）. The experimental results reveal that the proposed bit-parallel multiplier saves about 65% space complexity and 33% time complexity as compared to the traditional multipliers for a general polynomial and dual basis of GF（2^m）.展开更多
文摘In general, there are three popular basis representations, standard （canonical, polynomial） basis, normal basis, and dual basis, for representing elements in GF（2^m）. Various basis representations have their distinct advantages and have their different associated multiplication architectures. In this paper, we will present a unified systolic multiplication architecture, by employing Hankel matrix-vector multiplication, for various basis representations. For various element representation in GF（2^m）, we will show that various basis multiplications can be performed by Hankel matrix-vector multiplications. A comparison with existing and similar structures has shown that time complexities. the proposed architectures perform well both in space and
文摘Recently, cryptographic applications based on finite fields have attracted much attention. The most demanding finite field arithmetic operation is multiplication. This investigation proposes a new multiplication algorithm over GF（2^m） using the dual basis representation. Based on the proposed algorithm, a parallel-in parallel-out systolic multiplier is presented, The architecture is optimized in order to minimize the silicon covered area （transistor count）. The experimental results reveal that the proposed bit-parallel multiplier saves about 65% space complexity and 33% time complexity as compared to the traditional multipliers for a general polynomial and dual basis of GF（2^m）.
