◼ DLP (Discrete Logarithm Problem)
Given an element ax=x+x+...+x of some group as well as x itself, the problem to compute the factor a is called the discrete logarithm problem. In some groups this task is easy to perform (e.g. for integers), whereas it is very hard in others (e.g. groups of points on elliptic curves or Jacobians). Hence those groups are of special interest for cryptography.
As a matter of fact, even if it is clear that a collision enables the Discrete Logarithm Problem of y to the base g to be solved, given the discrete logarithm x, the fingerprint h = hml.yrl, and a message m2, it is likewise clear that r2 = rl + (ml-m2)/x mod q means that Hpk(ml; rl) = Hpk(m2; r2).
De fato, mesmo se estiver claro que uma colisão permite que o problema do logaritmo discreto de y à base g seja resolvido, dado o logaritmo discreto x, a impressão digital h = hml.yrl, e uma mensagem m2, é igualmente claro que r2 = rl + (ml-m2)/x mod q significa que Hpk(ml; rl) = Hpk(m2; r2).