Score:2

Solving $\mathsf{SVP}_{\gamma}$ in worst-case

in flag

What does it mean to solve $\mathsf{SVP}_{\gamma}$ in worst-case?

Does it mean that the problem is solvable for any lattice we choose?

Score:3
in flag

Solving $\text{SVP}$ in the worst-case means solving a 'hardest' instance of $\text{SVP}$. This isn't what we want for cryptography as we want problems to be hard to solve on average (average-case). Foundational problems like $\text{SIS}$ and $\text{LWE}$ are average-case problems depending on the hardness of worst-case problems like $\text{SVP}$, i.e. if $\text{SVP}$ is hard in the worst-case then $\text{LWE/SIS}$ are hard on average.

I recommend reading 'M. Ajitai. Generating Hard Instances of Lattice Problems' for more information on this.

Don Freecs avatar
sz flag
can you explain more, why average case is favorable in cryptography??
Mark avatar
ng flag
@DonFreecs it's just what shows up. When you randomly sample keys, often you are (implicitly) randomly sampling an instance of some underlying problem, so "breaking" things becomes an average-case problem. That being said, *precisely what* distribution to sample from can sometimes be hard to determine. The worst-case to average-case reduction people are discussing here helps identify the LWE distribution as "the right" one.
Score:1
sz flag

as far as I know, solving a problem in the worst case hardness means solving the problem for any instance given (hence for any distribution of instances) on the other hand, solving a problem in average case means solving this problem for a given distribution ...

"Correct me please I am wrong"

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