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I want to meet the 5 year old that can understand this.

Thanks I’ll have to brush up on my computer science theory before tackling this.

Your ELI5 needs an ELI5 :)

They're talking about computing k^m mod p. In the era where you can get a sense for what operations have taken place based on fingerprints left in the cache, timing, etc, the algorithms for computing it are ideally designed to be hardened against it. That is, given knowledge of the sorts of operations that have taken place, how many bits of the secret that is being computed can be recovered? They demonstrate that more bits than previously thought can be practicably recovered from an actual implementation of RSA by using clever statistical modeling and ideas from information theory.

This is much easier to digest, thank you. What's the significance of computing k^m mod p in this context?