# Research - Cryptography

## BN-Curves

This is a web-frontend to our database which contains some BN-curves. Each curve is an elliptic curve *E:Y*^{2}=*X*^{3}*+b* defined over **F**_{p} of prime order n and embedding degree *k*=12. The integer u determines the primes

*p=p(u)*=36*u*^{4}+36*u*^{3}+24*u*^{2}+6*u*+1,

*n=n(u)*=36*u*^{4}+36*u*^{3}+18*u*^{2}+6*u*+1

and trace of Frobenius *t(u)=*6*u*^{2}+1. A generator of the group *E*(**F**_{p}) is given by *G=(*1,*y)*.
The database contains amongst others curves where *p* has 160, 192, 224, 256, 288, 320, 352, 384, 416, 448, 480 and 512 bits.
Entering the desired number of bits or parameters u,b,y will give you a randomly selected curve from the database which has the requested properties.
Please enter the BN-curve parameters you need:

Entering a desired number of bits below will compute a new curve with that bitsize which is in general not in our database: