# Tagged Questions

Questions on cryptography and cryptanalysis, encryption and decryption, and the making and breaking of codes and ciphers. Consider posting your question at Cryptography.SE.

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### Are the sets $\left\{\sum_{x \in \operatorname{GR}(p^2,m)}w^{Tr(ax)} \right\}$ and $\left\{\sum_{x \in Z^m_{p^2}}w^{b \cdot x} \right\}$ equal?

Let $GR(p^2,m)$ be the Galois ring with $p^{2m}$ elements and characteristic $p^2$. Let $Z^m_{p^2}$ be the cross product of $m$ copies of $Z_{p^2}$ which is the set of integers from zero up to $p^2-1$....
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### Why is this prime a bad choice for the ElGamal cryptosystem?

Using the ElGamal cryptosystem in $\mathbb{Z}_{p}^{\times}$, the proposed prime is $p = 2^{1947}\cdot 5 + 1$. The exercise asks me to show why this is a poor choice, and I can't quite do it. In my ...
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### Application of fixed point theory in cryptography

Does fixed point theory has an application in Cryptography? I really don't know about Cryptography. If you mention any books on this matter it really helpful
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### RSA public encryption: Finding p and q given $\phi(pq)$

I have a quick question: My book asks me to show that if someone were to find that value of $\phi(pq)$ then they would be able to find out p and q. Is this possible? I've seen many examples of ...
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### How can I explain a Zero Knowledge Proof with minimal mathematics

I asked this earlier on how to explain a Zero Knowledge Proof to a layman. but I'm looking for a mathematical analogy that might "enhance" the superpower explanation. In that linked superpower, that ...
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### How to expand Diffie-Hellman key exchange for multiple users?

To provide OTR (off the record) security for XMPP group chats we've discussed an idea for a Diffie-Hellman key exchange algorithm for multiple users. It should work as follows: Choose a cyclic group ...
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### Efficiency of McEliece Cryptography

Most of the sources say McEliece has never gained acceptance because of its large size of private and public keys. However I have never heard about the size (or length) of its ciphertext. For example, ...
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### What if the p and q used in keys generation of Pailler cryptosystem are composite?

I've seen a few implementations of Paillier cryptosystem that uses probable primes to choose $p$ and $q$. Assuming that a keypair is generated with $p$ and $q$ that are coprime and that $pq$ is ...
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### Apply Pohling-Hellman to calculate the discrete logarithm

I am looking at the following example of calculating the discrete logarithm with Pohli-Hellman. The group is $\mathbb{F}_{29}^{\times}$ and we given $y=10$ and $g=3$. We want to find $0 \leq x \leq 28$...
### Solving for $m$ algebraically given $m^e \equiv c_1 \pmod n$ and $(\alpha m+\beta)^e \equiv c_2 \pmod n$
Given $m,n,e,c_1,c_2,\alpha,\beta \in \mathbb{N}$ and the system of congruences:  \begin{align} m^e \equiv c_1 &\pmod n &(1)\\ (\alpha m+\beta)^e \equiv c_2 &\pmod n &(2) \end{align} ...