An Automated Scheduler-Based Approach for the Development of Cryptoprocessors for Pairing-Based Cryptosystems

Pairings have been used to develop a wide range of cryptographic protocols to solve problems beyond the reach of traditional public-key cryptographic schemes. At the same time, they are mathematically complex and involve a rich hierarchy of operations over finite fields and extension fields. Performing a pairing operation involves large number of modular multiplications, additions, and subtractions that require cumbersome manual scheduling of operations. Due to large sequence of operations and custom hardware architectures designed for a specific pairing algorithm, it becomes infeasible to change the underlying pairing type, elliptic curves, or even parameter sets without redesigning the entire architecture. We present the design of a configurable and generic execution unit, capable of being used for any pairing algorithm, and serving as a coprocessor to perform all the underlying operations. The execution unit is supported by a software static scheduler to automate the process of manual scheduling of operations at the lowest level of hierarchy, i.e., at the level of prime field arithmetic. We develop a hierarchical input format to support the tower of fields used to represent extension field elements involved in pairings. We optimize the overall performance of the cryptoprocessor by using an optimal number of multiplier units, capable of taking full advantage of the parallelism present in the algorithm and a single modular adder/subtractor, working in parallel with multipliers.