Mathematics Stack Exchange
Mathematics Stack Exchange

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
16
votes
4 answers

How to break XOR cipher with repeating key?

I need to crack a stream cipher with a repeating key. The length of the key is definitely 16. Each key can be any of the characters numbered 32-126 in ASCII. The algorithm goes like this: Let's say you have a plain text: "Welcome to Q&A for people…
user8689
10
votes
1 answer

Cracking Playfair code

I need to crack a Playfair encoded text without knowing the keyword. While searching the internet I found a way to do this using a 'shotgun climbing hill' method. Problem is, I can't decide how to quantify one solution against the other. I'm pretty…
KevinDL
  • 1,816
9
votes
3 answers

Cube roots modulo $p$

Let $a$ be a positive integer. Is there any general method of solving equations of the form $$x^3\equiv a$$ modulo $p$, where $p$ is a prime number? Here are two examples: Example 1: In $\mathbb{Z}_{13}^*$ (using multiplication as our binary…
Moses
  • 161
9
votes
3 answers

Is it possible to guess an AES key from a series of messages encrypted with that key?

I was wondering if it is practically achievable to guess an AES key from a large number of short messages encrypted with that key, the attacker knowing the exact content of every message. Suppose the messages are very short (one block), and quite…
gd1
  • 569
8
votes
1 answer

has any cycle found in MD5?

We are not sure whether MD5 has fixed point or not. But since the sample space is finite, it must have cycles: $$ A →(MD5)→ B →(MD5)→ C →(MD5)→ D →(MD5)→ A $$ Has any research been done on MD5 to find cycles? What caused I think about it is that…
gerrnar
  • 81
7
votes
5 answers

Is every encryption a bijective function?

Is there any encryption algorithm that is not bijective function ? Should an encryption always give the same result given same key ?
iKid
  • 237
6
votes
3 answers

Should RSA public exponent be only in {3, 5, 17, 257 or 65537} due to security considerations?

In my project I'm using the value of public exponent of 4451h. I thought it's safe and ok until I started to use one commercial RSA encryption library. If I use this exponent with this library, it throws exception. I contacted developpers of this…
Vladislav Rastrusny
  • 163
6
votes
2 answers

RSA signature system

Alice wants to construct a RSA signature system to sign messages. The system is secure if the measure $n$ is a product of two primes, each of them has two digits. Describe the construction of the keys. Describe how Alice signs the message…
Mary Star
  • 13,956
5
votes
0 answers

A special case of zero-knowledge computation

This question is inspired by the disappearance of Malaysian Air 370. Let's suppose the plane crashed into the ocean. These are hotly contested waters where various countries (US, China, India, others) probably have listening devices (hydrophones)…
Llaves
  • 161
4
votes
1 answer

RSA-keys are not good?

PK := (n, e) = (1765937, 23755) SK := (n, d) = (1765937, 1734043) Can someone tell me, given these keys, what is not good about them, meaning it should not be very difficult to break it? (Except from the fact that they are very small numbers.)
tr3quart1sta
  • 141
4
votes
1 answer

Square roots in modular arithmetic

Suppose $n = pq$ with $p$ and $q$ both primes. Suppose that $\gcd(a, pq) = 1$. Prove that if the equation $x^2 ≡ a \bmod n$ has any solutions, then it has four solutions. Suppose you had a machine that could find all four solutions for some given…
leeha
  • 157
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  • 5
4
votes
1 answer

Solving $x^y + y^x = a$

If $a$ is given how can I calculate $x^y$ and $y^x$ the fastest way? Is there any other way than brute forcing? How is this type of equation called? Let's say $x$ and $y$ must be $>1$ and non negative integers.
arminb
  • 317
4
votes
2 answers

How valid is the concern over narrow pipe cryptographic hash function designs?

Narrow pipe hash function designs have recently come under fire, particularly in reference to some SHA-3 candidates. Is this criticism valid? Can it be explained more simply than this paper does?
Omnifarious
  • 235
4
votes
1 answer

How to add two points on an elliptic curve

How do you add two points P and Q on an elliptic curve over a finite field $\Bbb F_{p}$. For example: adding the points $(1,4)$ and $(2,5)$ on the curve $y^2 = x^3+2x+2$ over $\Bbb F_{11}$. I know one way involves drawing a straight through the two…
badosky
  • 123
4
votes
1 answer

Secret sharing for a general access structure

A secret sharing scheme is a method of distributing finite pieces of information (called shares $\alpha_i$) among a set of players $P=\{1,\ldots, k\}$ in such a way that only certain subsets of players $S \subseteq P$ (the authorized coalitions) can…
suitangi
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