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.

'Something That Unites Us All': Understandings of St. Patrick's Day Parades as Representing the Irish National Group

<p>The present study investigates how attendees at national celebratory crowd events-specifically St. Patrick's Day parades-understand the role of such events in representing and uniting the national community. We conducted semi-structured interviews with people who attended St. Patrick's Day parades in either Dublin or Belfast. In year 1, full-length interviews were conducted before and after the events (N=17), and in years 1 and 2, shorter interviews were conducted during the events (year 1 N=170; year 2 N=142). Interview data were analysed using thematic analysis, allowing the identification of three broad themes. Participants reported that (i) the events extend the boundary of the national group, using participation to define who counts as Irish; (ii) the events strategically represent the nature of the national group, maximising positive images and managing stereotypical representations; and (iii) symbolism serves to unify the group but can also disrupt already fragile unity and so must be managed. Overall, this points to a strategic identity dimension to these crowd events. We discuss the implications of these findings for future research in terms of the role of large-scale celebratory events in the strategic representation of everyday social identities.p>