# 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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### How to solve a modular inequality with optimization?

I have this: $x\le y$ $y\lt m$ $x^2\mod m < y$ $y$ and $m$ are given. I am trying to maximize the value of $x$. Any advice on how to approach this?
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### On Pohlig-Hellman prime power discrete logarithm algorithm

If $p,q$ are odd primes and suppose we know $x\bmod 2^rp^tq^u$ in $g^x=h\bmod q$ where $2^{r+1}p^{t+1}q^{u+1}|\phi(q)$ and $g$ generates $\Bbb Z_{n}^\times$ then what is the procedure and complexity ...
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### Conditions for existence of quadratic residue congruent to 1

Under what conditions are we guaranteed an existence of quadratic residue 1 other than squares of 1 and -1. What conditions a number must satisfy to have such residue.
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### What is the bank need to get the message?

In Number theory $p=37, q= 43$, $\phi(pq)= 36 \cdot 42$, $e=5$ $d=?$ What does the bank need to get the message? I don't understand this problem. Can any one help me please?
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### Security of $(k, 2k)$-bit generator for small seeds

Here is the problem I am working on for context. I have $\epsilon \le 1 - 2^{-k}$ and $\epsilon$ approaches 1 as $k \to \infty$ but I'm stuck on part c). The $f$ is secure iff there does not exist ...
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### Connection between quadratic residue of a number to its factors'

Is it true that, If $N$ is product of two coprime numbers greater than 1. Quadratic residues of these numbers are quadratic residue of $N$ and vice versa? Can someone point me to a proof or show me if ...
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### Proof of $a^{m \, \pmod{\varphi(n)}} \equiv a^m\pmod n$

I am currently studying modular arithmetic for a course in cryptography. I have proved many operations, but I am stuck in one: Assume $n,a\in \mathbb{N}$ and $n\ge 2$. Prove that if $\gcd(a,n)=1$ ...
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### Monoalphabetic Cipher

I am not sure how to get the key for the following Monoalphabetic Cipher question. This is a textbook question and I know the answer, but I juts dont know how they got the key. Question: ...
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### Encryption - show probability for obtaining specific bit

Assume a person A encrypts a message which consist of the bits m1, ..., mn. The person is using the one-time pad algorithm. Another person B intercepts the ciphertext and we suppose he knows that mi (...