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No, it will not get easier and this is easy to see. Since p is public, everybody can make arbitrary many instances of a DL system with that p. You cannot diminish complexity by that means. If you could, such a scheme would bem consideed as broken or at least assigned a lower complexity in the first place.


Shor's method relies on a period finding routine on a quantum computer. A function $f: (x_1, \dots, x_n) \mapsto f(x_1, \dots, x_n)$ is periodic, of period $(\omega_1, \dots, \omega_n)$, if $f(x_1 + \omega_1, \dots, x_n + \omega_n) = f(x_1, \dots, x_n)$ for all tuples $(x_1, \dots, x_n)$ in the domain of $f$. Factorization problem Given an RSA modulus $...

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