, , vol.1
,
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, 1, modulo is at negligible distance of the uniform and is independent of modulo . So even if an unbounded adversary can learn modulo from ?, modulo remains at negligible distance of the uniform from his point of view and ? + perfectly hides ? ? Z/ Z. Therefore: |P
Let be an adversary for the HSM problem, its advantage is defined as: 1. Let ? be the bit size of . Pick?a random ?(?) ? ? bits prime such that?? ? ,
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Modulus Expo. (ms) Keygen (ms) Signing (ms) Keygen (b) Signing (b), p.112 ,
Discriminant Expo. (ms) Keygen (ms) Signing (ms) Keygen (b) Signing (b), p.112 ,
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, If gets as input an element of whatever the value of ? * , * follows the uniform distribution modulo and is independent of . So 's success probability in outputting
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