How do you derive the lambda and beta values for endomorphism on the secp256k1 curve?
You can see a little background about this on this bitcointalk post by the late Hal Finney.
Beta and lambda are the values on the secp256k1 curve where:
λ^3 (mod N) = 1
β^3 (mod P) = 1
As seen here, in hex, N and P are:
N = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141
P = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F
The actual values of lambda and beta are easily verifiable and are:
λ = 5363ad4cc05c30e0a5261c028812645a122e22ea20816678df02967c1b23bd72
β = 7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee
The question for me is, how do you derive this? Can someone show me step-by-step how you can figure out these values?