Supercomputing,You seem to be mistaken:
SourceLet us summarize: in the prime case the domain parameters are (p,a,b,G,n,h) and in the binary case they are (m,f,a,b,G,n,h)The prime field contains a prime in the domain parameters, but the binary does not. Prime based curves use
p as the prime generating the security as you stated, Binary curves use
m and f. Coinshield uses sect571r1 which is a NIST/SECG curve over a 571 bit binary field
For sect571r1 domain parameters (m,f,a,b,G,
n,h),
n is a large prime.
Please post your sources, otherwise this is conjecture.
Thank You,Viz.Number theory (IFP, ECDLP, IQF) is my area of research.
NIST-B571
http://web.mit.edu/Ghudson/dev/third/mozilla/security/nss/lib/freebl/ecl/ecl-curve.hBase point subgroup order (hex):
03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF\
FFFFFFFFFFFFFFFFFFFFFFFFE661CE18FF55987308059B18\
6823851EC7DD9CA1161DE93D5174D66E8382E9BB2FE84E47