Fast Software Implementations of Finite Field Operations

Software implementation of finite field operations is becoming more and more widely used in communication, cryptography and multimedia applications. It is more flexible and easier to deploy, compared to dedicated hardware component. However, finite field operations often become the bottle-neck for high throughput applications and are impacting the life time of power constrained devices. It is thus desirable to keep pushing the efficiency of their implementation. In this paper, we describe several improvement techniques to increase the throughput of finite field operations without incurring extra complexity. Maintaining pre-computed tables to simplify operation and improve performance is a common practice [3]. In finite field operations, modular operation and conditional branch (if· · · then) are frequently used. These operations are very expensive in computation compared to table look-up. In this paper, we explore the idea of precomputation to a new depth and replace these operations with simpler ones, using moderately larger memory, which is usually not an issue in most platforms. We propose to use augmented table to eliminate modular operation and conditional branch completely. Simulation results show that the best improvement approach reduces execution time of finite field multiplication and division by about 67% and increases the encoding throughput of Reed-Solomon (RS) [4] code about 3 times. We also show that there is limitation in trading memory usage for efficiency: when complete precomputation and extra large table are used, the throughput of finite field operations degrades instead.