Twisted Edwards Curve / Montgomery

[ineiti]

The current kyber ed25519 implementations seem to both use Twisted Edwards Curve, as proposed in the RFC8032:

• curve25519 is the variable-time, fast implementation - not used
• ed25519 is the constant-time, slower implementation - used in cothority

Unfortunately the popular BouncyCastle library uses Montgomery representation, as described in the RFC7748, but BouncyCastle doesn't support Twisted Edwards Curve representation.

So, we either:

• implement Twisted Edwards Curve in BouncyCastle or
• implement a Montgomery (RFC7748?) compatible curve25519 for dedis/kyber

Things to verify:

• Twisted Edwards Curve and Montgomery definitions in RFCs
• Compatibility of kyber/ed25519 with RFC8032
• Availability of Montgomery implementation in golang
• Why does golang use Twisted Edwards Curve representation per default?