I just started to study lattice Cryptography.
I'm now studying worst-case to average-case reduction for SIS.
In previous question, "worst means any and average means random".
And I wonder why the Shortest Independent Vectors Problem(SIVP) is the worst-case problem.
And, does SIVP means that
"For 'any' given lattice basis B, it is hard to find n linearly independent short vectors in L(B)"?
The definitions that I saw didn't have the word 'any'.
Does the word 'any' is involved in the sentence even though it is not explicitly mentioned? I'm guessing that SIVP is a worst-case problem because of 'any'.
If it is correct, does
"For a given 'randomly' chosen lattice basis B, it is hard to find n linearly independent short vectors in L(B)"
is an average-case problem?