General questions about the coursework with the implementation of the Schnorr EDS?

Question

Electronic digital signature

Good afternoon!
They set a coursework on the topic "Software implementation of a simplified version of Schnorr's EDS", I found an algorithm on the wiki.
Link to wiki
- Can you tell me if it's simplified?
- Large numbers are used there (1024 bits long), how can you perform actions with them?
- I also see there two types of some kind of EDS: an authentication protocol and a digital signature protocol, as I understand it, EDS is exactly the second option, i.e. Do I need to sign a message?
Also in this article small values, for example they say -

A prime number p is chosen, which is usually 1024 bits in length.

, and in the example they use p=48731 , should I ask the teacher about the size of the number or already fiddling with huge numbers?

Answer 1

Large numbers are used there (1024 bits long), how can one perform actions with them?

https://ru.wikipedia.org/wiki/Long_arithmetic (also the English term arbitrary-precision arithmetic). Google ready-made libraries that implement arbitrary-precision arithmetic.

the example uses p=48731

- this number fits in 16 bits, but it also fits in 1024 bits. Moreover, the numbers 0 and 1 also fit in 1024 bits. :) Large numbers are needed for greater crypto-strength. For example and for educational purposes, not very large numbers are enough. Yes, it's best to ask your teacher for clarification. If the teacher allows you to make an implementation, for example, for 32 bits, then you won’t have to mess around with long arithmetic libraries - this will save you time.