You might see examples of prime factorizations of large integers, or sorting huge lists of complex data structures, and those are certainly long running operations.
A new sequential digital multi-signature scheme and a new broadcasting digital multi-signature scheme are proposed based on the difficulty assumption of factoring and quadratic residues.
Answering a factorization challenge is proof that the respondent has done a quantifiable degree of work (or obtained the factors surreptitiously from the person who generated the composite).
Answering a factorization challenge is proof that the respondent has done a quantifiable degree of work (or obtained the factors surreptitiously from the person who generated the composite).