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How should attacker choose $m_1$ to be able to calculate advantage of adversary exactly? Well, for $p$ prime, then precisely $q$ of the values in $(1, p-1)$ will be Quadratic Residues and the precisely $q$ will not be; furthermore, there is one value ($0$) that resides outside the group (and hence is also an impossible value for $h^r$). Hence, if he ...
I assume this is homework (I have time imagining that this is a problem that you need to solve; if it is, turn "use real RSA padding"). Since this is assumed to be homework, I'll give you the initial steps, and let you do the rest of the work. First off, what you're asking is to find a value $m$ such that \$(m^3 \bmod n) \bmod 2^{136 } = \text{"\x00"...