- Normal Basis: Choose the Type T low-complexity normal basis with the smallest T.
For each binary field, the parameters are given for the above basis representations.
1.4 Choice of Curves
Two kinds of curves are given:
- Pseudo-random curves are those whose coefficients are generated from the output of a seeded cryptographic hash. If the seed value is given along with the coefficients, it can be verified easily that the coefficients were indeed generated by that method.
- Special curves whose coefficients and underlying field have been selected to optimize the efficiency of the elliptic curve operations.
For each size, the following curves are given:
- A pseudo-random curve over GF(p).
- A pseudo-random curve over GF(2m).
- A special curve over GF(2m) called a Koblitz curve or anomalous binary curve.
The pseudo-random curves are generated via the SHA-1 based method given in the ANSI X9.62 and IEEE P1363 standards. (The generation and verification processes are given in Appendices 6-4 through 6-7.)
1.5 Choice of Base Points
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