Is possible to create a custom curve like Curve448/Ed448 in Botan?

[gb-jose]

I am trying to do some curve elliptic operations over Curve448/Ed448. I defined the EC_Group object to register the curve, but I am not able to pass the group verification.

const Botan::BigInt p("0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffff");
const Botan::BigInt a("0x262a6");
const Botan::BigInt b("0x01");
const Botan::BigInt n("0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffff7cca23e9c44edb49aed63690216cc2728dc58f552378c292ab5844f3");
const Botan::BigInt g_x("0x05");
const Botan::BigInt g_y("0x7d235d1295f5b1f66c98ab6e58326fcecbae5d34f55545d060f75dc28df3f6edb8027e2346430d211312c4b150677af76fd7223d457b5b1a");
const Botan::BigInt h("0x04");
const Botan::OID oid("1.3.101.111");

// create EC_Group object to register the curve
Botan::EC_Group ec_group(p, a, b, g_x, g_y, n, h, oid);

Botan::AutoSeeded_RNG rng;

if(!ec_group.verify_group(rng)) {
    std::cout << "Does not work!" << std::endl;
    return 1;
} else {
    std::cout << "Works" << std::endl;
}

Parameters taken from: https://neuromancer.sk/std/other/Curve448

[randombit]

Ed448 and X448 are already supported, but not through EC_Group - that interface is exclusively used for Weierstrass curves. If you just need signatures and key exchange, the dedicated interfaces (eg Ed448_PrivateKey) is certainly the preferred approach.

It is possible to map Edwards and Montgomery curves to Weierstrass coordinates; see https://crypto.stackexchange.com/questions/27842/edwards-montgomery-ecc-with-weierstrass-implementation and https://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.800-186.pdf (specifically the specifications of W-25519 and W-448) and this should work with EC_Group and related types, but this has not been tested by me or AFAIK anyone else.

Do you actually need generic point arithmetic here? If so can you please share what sort of application you are working on.

[gb-jose]

Thanks for the quick response!