Formal verification is fundamental in many phases of digital systems design. The most successful verification procedures employ Ordered Binary Decision Diagrams (OBDDs) as canonical representation for both Boolean cir...Formal verification is fundamental in many phases of digital systems design. The most successful verification procedures employ Ordered Binary Decision Diagrams (OBDDs) as canonical representation for both Boolean circuit specifications and logic designs, but these methods require a large amount of memory and time. Due to these limitations, several models of Decision Diagrams have been studied and other verification techniques have been proposed. In this paper, we have used probabilistic verification with Galois (or finite) field GF(2m) modifying the CUDD package for the computation of signatures in classical OBDDs, and for the construction of Mod2-OBDDs (also known as ?-OBDDs). Mod2-OBDDs have been constructed with a two-level layer of ?-nodes using a positive Davio expansion (pDE) for a given variable. The sizes of the Mod2-OBDDs obtained with our method are lower than the Mod2-OBDDs sizes obtained with other similar methods.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
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
文摘Formal verification is fundamental in many phases of digital systems design. The most successful verification procedures employ Ordered Binary Decision Diagrams (OBDDs) as canonical representation for both Boolean circuit specifications and logic designs, but these methods require a large amount of memory and time. Due to these limitations, several models of Decision Diagrams have been studied and other verification techniques have been proposed. In this paper, we have used probabilistic verification with Galois (or finite) field GF(2m) modifying the CUDD package for the computation of signatures in classical OBDDs, and for the construction of Mod2-OBDDs (also known as ?-OBDDs). Mod2-OBDDs have been constructed with a two-level layer of ?-nodes using a positive Davio expansion (pDE) for a given variable. The sizes of the Mod2-OBDDs obtained with our method are lower than the Mod2-OBDDs sizes obtained with other similar methods.
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）.
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
