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The Pohlig-Hellman algorithm reduces the discrete logarithm from a group of composite order to subgroups of prime order. For instance, with an elliptic curve and a point $P$ whose order is a composite integer $q = p_1 \cdot p_2$, and we want to find $k$ such that $Q = [k]P$ for a given point $Q$. Then, since $[p_2]P$ is a point of order $p_1$. Let $$ Q_2 = [...


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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 ...


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If you have $e$ ciphertexts for the same message, then the attack is the same, you just have to apply the CRT with $e$ values, then computing the $e$'th root of the resulting value might need some work. And this is assuming that all moduli are relatively prime of course. If that's not the case, there is $i,j$ and $gcd(N_i, N_j) \neq 1$. So you can factor ...


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This question is about the properties of the bitwise eXclusive-OR operator (also known as XOR or $\oplus$), which is very common in cryptography. It's the bitwise operator for the similarly named and noted bit operator XOR, which truth table is $$\begin{array}{c|c|c|c|c|c} \text{first/left input}&a&0&0&1&1\\ \text{second/right input}&...


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I'm somewhat new at this, so there might be a better way to solve this, but this is how I solved it. If I understand right, the extra parameter given is written as: $$\mathtt{}({e}_{1} \oplus k) \oplus ({e}_{2} \oplus k) = e_{3} \oplus k$$ (that is, the decoded contents of e1 xor'd with the decoded contents of e2 is equal to the decoded contents of e3) The ...


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Normal DES Let's say you have a normal DES plaintext-ciphertext pair encrypted with 56 bits key $k$ where $C_1=DES_k(P_1)$. In the worst case, one needs to try the $2^{56}$ possible keys to find the encryption key. And later on, one can decrypt all Ciphertext encrypted with the key $k$ DESA Let's say one has 2 pairs of plaintext-ciphertext pairs ecnrypted ...


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I emailed someone, and it turns out that the rotor positions found by the Bombe are used as the ring setting in the checking machine. Because the ring setting is the "negative" of the rotor position, the indicator drums spin backwards, so that it shows the correct ring setting that corresponds to the rotor positions for the checking machine.


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I didn't want to delete this question, but it seems like after pondering this for a week I finally understand right when I seek help online. When the ring setting and the rotor position all increase by the same amount, they cancel and so the ring pretty much stays the same. Although the contact points of the ring to the alphabet ring is different, it makes ...


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