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.

Incidence of Type 1 Diabetes in Sweden Among Individuals Aged 0–34 Years, 1983–2007:An analysis of time trends

OBJECTIVE: To clarify whether the increase in childhood type 1 diabetes is mirrored by a decrease in older age-groups, resulting in younger age at diagnosis.
RESEARCH DESIGN AND METHODS: We used data from two prospective research registers, the Swedish Childhood Diabetes Register, which included case subjects aged 0-14.9 years at diagnosis, and the Diabetes in Sweden Study, which included case subjects aged 15-34.9 years at diagnosis, covering birth cohorts between 1948 and 2007. The total database included 20,249 individuals with diabetes diagnosed between 1983 and 2007. Incidence rates over time were analyzed using Poisson regression models.
RESULTS: The overall yearly incidence rose to a peak of 42.3 per 100,000 person-years in male subjects aged 10-14 years and to a peak of 37.1 per 100,000 person-years in female subjects aged 5-9 years and decreased thereafter. There was a significant increase by calendar year in both sexes in the three age-groups <15 years; however, there were significant decreases in the older age-groups (25- to 29-years and 30- to 34-years age-groups). Poisson regression analyses showed that a cohort effect seemed to dominate over a time-period effect.
CONCLUSIONS: Twenty-five years of prospective nationwide incidence registration demonstrates a clear shift to younger age at onset rather than a uniform increase in incidence rates across all age-groups. The dominance of cohort effects over period effects suggests that exposures affecting young children may be responsible for the increasing incidence in the younger age-groups.