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At this point, how does the attackers system know it has broken the encryption, especially if it has attempted many previous attempts & at insane speeds? Corollary: how can an attacker know they have decrypted successfully since the decrypted text would look exactly like encrypted text of the next layer of encryption? It doesn't. But note that to verify ...


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The answer is not easy, however, a good starting point is Florent Chabaud and Antoine Joux's paper on SHA-0 and SHA-1 Differential Collisions in SHA-0, Crypto 1998. Simple Introduction In, MD4, SHA-0,SHA-1, and SHA-2 there is a compression function. $$C:\{0,1\}^\ell \to :\{0,1\}^n$$ where $n$ is the output size and $\ell$ is the block lenght to process. ...


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I can only give a very simple-minded answer. In N. David Mermin's Quantum Computer Science: An Introduction, in his explanation of RSA encryption in Section 3.3, he says Efficient period finding is of interest in this cryptographic setting not only because it leads directly to efficient factoring (as described in Section 3.10), but also because it can lead ...


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For an RSA modulus, Shor's algorithm will (with high probability) return a large factor of the multiplicative order of some base element modulo $N$. Various adjunct classical algorithms can use this to return the factors of $N$, but equally one could directly use this output to compute an effective decryption exponent without bothering to compute the factors....


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