Week 11 homework for Uncloak CryptoEng course
Exercise implementation of Shanks Baby-step giant-step for arbitrary groups. No optimizations were kept in mind for it. The idea
is to create a function which would work with any group, so
it needs to be provided with information about the group itself (operation and inverse) and the order of the element
that was exponentiated.
Review
https://discord.com/channels/1031896857074475059/1031917142578311229/1075861221993087146
A couple quick notes: your algorithm to compute exponents is linear in the size of the exponent; it could be logarithmic by using the fast-powering algorithm. You could be using the Fn in place of fn; fn could be FnMut, FnOnce, or Fn, or even just implement shank step as a method over a Group struct, with defined methods for operation and inverse, though your impl is nice self-contained for a proof of concept. You could compute both baby-steps and giant-steps in the same loop; you could store the values for index (Value -> Index, not the other way around) and value in a pair of hashmaps, and check at each addition whether the value already existed in the other hashmap, and terminate early if found. Finally, cargo clippy would find some generic lints.