PBC Library Manual 0.5.11 - Stanford Crypto Group

Chapter 8. PBC internals
b:
E: y^2= x^3 + b
beta:
A quadratic nonresidue in Fq: used in quadratic extension.
alpha0, alpha1:
x^6 + alpha0 + alpha1 sqrt(beta) is irreducible: used in sextic extension.
Discovered by Barreto and Naehrig, "Pairing-friendly elliptic curves of prime order".
8.9. Type G Internals
Another construction based on the CM method.
g_param struct fields:
q, n, h, r:
h * r = n is the order of E(F_q)
a, b:
E: y^2 = x^3 + ax + b
nk:
#E(F_q^10)
hk:
hk * r^2 = nk
coeff:
array of coefficients of polynomial used for quintic extension.
nqr:
a quadratic nonresidue
g_param struct fields:
Discovered by Freeman, "Constructing pairing-friendly elliptic curves with embedding degree 10."
8.10. Testing functions
For testing, debugging, demonstrations and benchmarks. Declared in pbc_test.h:
void pbc_demo_pairing_init(pairing_t pairing, int argc, char **argv)
Initializes pairing from file specified as first argument, or from standard input if there is no first argument.
40