# 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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### cryptographic hash functions

Suppose $โ: ๐\to ๐$ is a hash function. For any $๐ฆ\in ๐$ , let $โ^{โ1}(๐ฆ)=\{๐ฅ:โ(๐ฅ)=๐ฆ\}$ and denote $๐ ๐ฆ=|โ^{โ1}(๐ฆ)|$. Define $๐=|\{\{๐ฅ_1,๐ฅ_2\}:โ(๐ฅ_1)=โ(๐ฅ_2)\}|$. Note that N counts the ...
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### Proposed two key cryptography

Q1. I do not understand why e should be public? It may be more secure to keep it private and known only to the sender and receiver. Q2. I need comments on the following proposed algorithm: Both ...
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### Generator of group, Computation of discrete logarithm

The prime number $p=67$ is given. Show that $g=2$ is a generator of the group $\mathbb{Z}_p^{\star}$. Compute the discrete logarithm of $y=3$ as for the base $g$ with Shanks-algorithm. Compute the ...
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### Given plaintext and ciphertext of the same length, how could one generate potential symmetric keys if encryption algorithm is unknown?

This question is about both encryption and about how and if one could transform data from one given form to another given form and back. I am given plaintext and ciphertext, both of which are the ...
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### Latin Squares and Olderogge Code

So I have two Latin Squares, $A$ and $B$ that form a pair of MOLS of order $m$. I then have an Olderogge code formed from $A$ and $B$, where each binary vector of length $m^2$ is encoded as a codeword ...
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### Primitive vs Irreducible

Are all irreducible polynomials primitive? If not can anyone give an example of such a polynomial that is irreducible but not primitive?
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### Algorithms for Performing Large Integer Matrix Operations w/ Numerical Stability

I'm looking for a library that performs matrix operations on large sparse matrices w/o sacrificing numerical stability. Matrices will be 1000+ by 1000+ and values of the matrix will be between 0 and ...
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### A variant of the “closest vector problem” (CVP) in lattice-based cryptography

Consider a public-key scheme on lattices, such as GGH. The private key is a basis $\mathbf{B} \in \mathbb{Z}^{m \times n}$ of a lattice $\mathcal{L}$ with good properties (such as short nearly ...
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### Finding the random $r$ in a Paillier encrypted message with knowledge of the private key.

In the Paillier cryptosystem, suppose that I know a Ciphertext encrypted with some unknown random $r$ i.e. $$C = (g^m r^n) \bmod n^2$$ I know $g, n$, the prime factorization of $n$, i.e., $pq$. I ...
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### Effect of seeds on the generation of keystream from a LFSR

I have a question regarding something I noticed about LFSR seeds. I tried different seeds in a simple LFSR with polynomial of โx4+x+1โ, most cases I got equal amount of 1s and 0s in the keystream ...
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### dining metaphysicians

I thought I'd read about this problem years ago, but cannot find the answer online. There is a more well-known dining philosophers problem that is vaguely similar. https://en.wikipedia.org/wiki/...
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### Discrete Logarithm vs Integer Factorization

Can anyone please tell me if finding discrete logarithm is considered more difficult than integer factorization? We have very advanced methods to find factors of large composite numbers like Number ...
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### Need help in Hashing to create a fingerprint

Given a pattern P of length m and a text T of length n (n >= m), in which all characters ...
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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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### Why the light contrast of a set $\mathcal{E}$ of VCRG produced by an encryption scheme for a binary image B is defined as follows

In the paper "Image encryption by multiple random grids, Shyong Jian Shyu, 42(7):1582-1596 ยท July 2009" here, the light contrast of a set $\mathcal{E}$ of VCRG produced by an encryption scheme for a ...
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### Brute force through the DiffieโHellman key exchange

I was reading about DiffieโHellman key exchange example on wikipeida: Alice and Bob agree to use a modulus $p = 23$ and base $g = 5$ (which is a primitive root modulo 23). Alice chooses a secret ...
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### If $n$ is divisible by a perfect square then $n$ is not a Carmichael number.

If $n$ is divisible by a perfect square then $n$ is not a Carmichael number. Going through the proof from Neal Koblitz's A Course in Number Theory and Cryptography...I am facing some difficulties to ...