FPGA montgomery modular multiplication architectures suitable for ECCs over GF(p)

New FPGA architectures for the ordinary Montgomery multiplication algorithm and the FIOS modular multiplication algorithm are presented. The embedded 18×18-bit multipliers and fast carry look-ahead logic located on the Xilinx Virtex2 Pro family of FPGAs are used to perform the ordinary multiplications and additions/subtractions required by these two algorithms. The architectures are developed for use in Elliptic Curve Cryptosystems over GF(p), which require modular field multiplication to perform elliptic curve point addition and doubling. Field sizes of 128-bits and 256-bits are chosen but other field sizes can easily be accommodated, by rapidly reprogramming the FPGA. Overall, the larger the word size of the multiplier, the more efficiently it performs in terms of area/time product. Also, the FIOS algorithm is flexible in that one can tailor the multiplier architecture is to be area efficient, time efficient or a mixture of both by choosing a particular word size. It is estimated that the computation of a 256-bit scalar point multiplication over GF(p) would take about 4.8 ms.

Dense pixel matching between unrectified and distorted images using dynamic programming

In this paper, a novel framework for dense pixel matching based on dynamic programming is introduced. Unlike most techniques proposed in the literature, our approach assumes neither known camera geometry nor the availability of rectified images. Under such conditions, the matching task cannot be reduced to finding correspondences between a pair of scanlines. We propose to extend existing dynamic programming methodologies to a larger dimensional space by using a 3D scoring matrix so that correspondences between a line and a whole image can be calculated. After assessing our framework on a standard evaluation dataset of rectified stereo images, experiments are conducted on unrectified and non-linearly distorted images. Results validate our new approach and reveal the versatility of our algorithm.

Parallel Programming of General-Purpose Programs Using Task-Based Programming Models

The prevalence of multicore processors is bound to drive most kinds of software development towards parallel programming. To limit the difficulty and overhead of parallel software design and maintenance, it is crucial that parallel programming models allow an easy-to-understand, concise and dense representation of parallelism. Parallel programming models such as Cilk++ and Intel TBBs attempt to offer a better, higher-level abstraction for parallel programming than threads and locking synchronization. It is not straightforward, however, to express all patterns of parallelism in these models. Pipelines are an important parallel construct, although difficult to express in Cilk and TBBs in a straightfor- ward way, not without a verbose restructuring of the code. In this paper we demonstrate that pipeline parallelism can be easily and concisely expressed in a Cilk-like language, which we extend with input, output and input/output dependency types on procedure arguments, enforced at runtime by the scheduler. We evaluate our implementation on real applications and show that our Cilk-like scheduler, extended to track and enforce these dependencies has performance comparable to Cilk++.