This has also bugged me in the case of other cryptographic algorithms, for example SHA-1 has several magic input constants, whose choice is not obvious. When ca

This has also bugged me in the case of other cryptographic algorithms, for example SHA-1 has several magic input constants, whose choice is not obvious. When casually reading through the original papers I could not find a clear explanation of how those values were chosen. Pretty much everything in the design seems fairly arbitrary and amendable to variation. In physics there are multiple case where you can do seemingly very hard calculations, if you do it in the wrong coordinate system and neglect symmetries that are present, that collapse to almost nothing (In the case of elliptic curves that was the fact that the curve points chosen by NSA were related by Q = P + e, where e was some point on the curve only known to the NSA)