# prime field

## prime field

[′prīm ′fēld]
(mathematics)
For a field K with multiplicative unit element e, the field consisting of elements of the form (ne)(me) -1, where m ≠ 0 and n are integers.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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A smart kick from youngster Harri Millard saw the centre and winger Blaine Scully bundle Cooney into touch deep in the Ulster 22, giving the Welsh side prime field position.
In the case of prime field arithmetic the Montgomery Parameter r will be r [equivalent to] [2.sup.k] mod p, so r can be calculated as two's complement of p as bitwise inverse of the given modulus plus 1.
Our previous work [33] already showed the differences between the efficiency of prime field based and field of characteristic 2 based elliptic curve systems in limited devices.
That was when his 70-yard punt earned prime field position, the hosts infringing on their own 22 and allowing the Kiwi to draw the sides level.
Dan Marshall's attempts to put Newcastle in prime field position were dashed when his kick went out on the full, Takulua having broken from his own 22 thanks to turnover ball in a half low on clear-cut chances.
The visitors took a 10-6 half-time lead when Price's brilliant positional kick handed them prime field position, Andy Unsworth applying the finish from close range.
The visitors assumed a 10-6 half-time lead when a 40-20 handed them prime field position, Andy Unsworth applying the finish.
Let k be a field which is finitely generated over its prime field. Let [P.sub.k] be the set of primes p for which k([C.sub.p]) is rational over k.
Again Ireland looked to have settled back into the game but an error gave the Knights possession in prime field position and Tom Burgess smashed his way over, Gale landing his second conversion.
When we compute the scalar multiplication on prime field, field inversion is a very expensive task as [i]/[m] is usually more than 30.
If they catch hint of an ambush they may continue to visit a prime field, but they will likely switch their pattern, visit it later or become nocturnal.
A Zach Arsenault rush put Nashoba in prime field position.

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