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Questions tagged [cryptography]

Questions on the mathematics behind cryptography, cryptanalysis, encryption and decryption, and the making and breaking of codes and ciphers.

Please only post questions about the mathematics of cryptography here.

  • Coding and implementation specific questions should go to Stackoverflow with encryption or cryptography tags.
  • You may also consider asking at Cryptography Stack Exchange which is for asking questions about the mathematics and properties of cryptographic systems, their analysis ("cryptanalysis") and subsidiary topics that generally make up cryptology.
1915 questions
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Perfect secrecy of hill cryptosystem

Let $H_{n\times n}$ matrix be a key for Hill cryptosystem over English alphabet. How can be proved that Hill cryptosystem is not perfectly secure? (Assuming that all messages are sent with the same probability.) What is the sufficient condition for…
pkotvan
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Problem about primitive root

Let p be a prime such that $q = \frac{p − 1}{2}$ is also prime. Suppose that g is an integer satisfying $g \not\equiv \pm 1 \pmod p$ and $g^q \not\equiv 1 \pmod p$. Prove that g is a primitive root modulo p.
leeha
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Primitive Root Theorem

Let $p$ be a prime and let $q$ be a prime that divides $p − 1.$ (a) Let $a \in F_p$ and let $b = a^{\frac{p−1}{q}}$. Prove that either $b = 1$ or else $b$ has order $q.$ (Recall that the order of $b$ is the smallest $k \ge 1$ such that $b^k = 1$ in…
leeha
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Real-world example for Diffie–Hellman key exchange

I read in Wikipedia about the Diffie–Hellman key exchange. But i can't imagine numbers which are hard to guess. Can anybody give me a real-world example for $p$, $g$ and the two random secrets?
wutzebaer
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ElGamal Digital Signature Scheme question

Use the ElGamal Digital Signature Scheme in the group $G$ = $F^{×}_{p}$ = where $p$ = $479$ is prime and $g$ = $13$. Your secret signing key is $x = 300$. If you choose an ephemeral key k = 11, what is the signature of your message m = 379? I…
SuprDooprPoopr
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What is the formula to estimate how long it can take to guess an OTP?

I was wondering if there is a formula to calculate how long it would take to "guess" a "X-Digit" OTP, presuming you limited the number of times you can try for each code and the number of codes you can get over a period of time. For example: I have…
Nicolas Bouvrette
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Cyber paper and pencil

Imagine that you would like to write down your passwords or other critical information into a sheet of paper. Could an algorithms without using a computer be so good as to avoid people of cracking it? There seems to exists some secret code messages…
Quora Feans
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Is such a cryptographic system possible?

Suppose you want to design a program that plays a card game (like Skat) for three players over the Internet. At the beginning of the game it is needed to deal the cards in a way, that each player gets the same amount of cards, but one must not know…
FUZxxl
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Is XOR distributive over any operations?

Given (A ^ C) * (B ^ C) = y where ^ is equivalent to XOR and * is equivalent to some operation (i.e. multiplication), is there any way of determining what A * B would have been equal to? It is assumed that you know A, B, C, and y, but that you don't…
James
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3 integer unknowns and 1 equation

All numbers are integers and none equate to 0. $$ 4=\frac{a}{b+c}+ \frac{b}{a+c} + \frac{c}{b+a} $$ My friend made this question, I tried to solve it for 2 hours and then he told me that I needed to use cryptology. I want to see how questions like…
John Smith
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Rijndael S-Box Permutation Group

Does the AES S-Box belong to the group of alternating permutions: A_{n} ? How does an identity S-Box effect the security of the algorithm?
user11393
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Extending the Diffie-Hellman protocol to multiple parties

I'm going through a Coursera cryptography class, and there appeared an interesting (and currently open) problem about extension of Diffie-Hellman protocol to multiple parties, while preserving the property of non-interactivity (i.e. no need for any…
DarkWanderer
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Decryption in the Merkle-Hellman cryptosystem

In a Merkle-Hellman cryptosystem, plaintext message units are of length $3$ over the alphabet $$ \begin{array}{cccc} &A&B&C&D&E&F&G&H&I&J&K&L&M&N&O \\ &0 &1 &2 &3 &4 &5 &6 &7 &8&9&10&11&12&13&14\\ \end{array} $$ $$ \begin{array}{cccc} …
kiwi
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RSA cryptography question

RSA user Alice has a public key ($n_A=pq$,$e_A$), where $p$ and $q$ are different primes such that the least common multiple $l$ of $p-1$ and $q-1$ is relatively small (i.e. $l$ is close to max($p-1,q-1$)). Explain why, even without factoring $n_A$,…
Swayy
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$16=m^{19} \mod 143$ - what is $m$

The background is RSA encryption. Can I use some theorem to exploit this situation? I thought about fermats theorem but I don t know how to use it here fermats theorem (If a and p are coprime numbers such that $a^{p−1} − 1$ is divisible by p, then p…
New2Math
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