I am examining the SPAKE2+ protocol introduced in Chapter 9 of a paper called The Twin Diffie-Hellman Problem and Applications. I noticing the use of a lot of syntax that looks like exponents. I am just becoming familiar with the mathematics behind the Diffie-Hellman protocol so forgive my ignorance, but does this imply the use of a modulus or are the exponents literally meant to be exponents alone?
but does the use of a modulus or are the exponents literally meant to be exponents alone?
Well, in SPAKE2+, all operations are done within some finite group, typically either a prime multiplicative group, or an elliptic curve group.
If we decide to use a prime multiplicative group, then yes, addition, subtraction and multiplication are all done implicitly modulo the prime (division needs to be computed differently, doing a school book division and then taking the modulus does not work).
Because this is so universal in cryptography, we generally don't insert all the 'mod p' operations (and if you're using an elliptic curve group, that wouldn't apply anyways)