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.
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Finding a primitive root of a prime number

How would you find a primitive root of a prime number such as 761? How do you pick the primitive roots to test? Randomly? Thanks
user27617
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Mathematically, why was the Enigma machine so hard to crack?

Mathematically, why was the Enigma machine so hard to crack? In laymen terms, what was it exactly that made cracking the Enigma machine such a formidable task? Everything I have seen about the Enigma machine, from a general article to information…
Daniel W. Farlow
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Would a proof to the Riemann Hypothesis affect security?

If a solution was found to the Riemann Hypothesis, would it have any effect on the security of things such as RSA protection? Would it make cracking large numbers easier?
Freeman
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Why are very large prime numbers important in cryptography?

Firstly, you guys are awesome, and I learn quite a bit just from reading the questions of others. Secondly, a friend asked me recently why large primes are important for data security, and I was unable to give him an answer with which I myself was…
sova
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What is an elliptic curve, and how are they used in cryptography?

I hear a lot about Elliptic Curve Cryptography these days, but I'm still not quite sure what they are or how they relate to crypto...
bdonlan
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Is there a way to find the log of very large numbers?

I should like to evaluate $\log_2{256!}$ or other large numbers to find 'bits' of information. For example, I'd need three bits of information to represent the seven days of the week since $\lceil \log_2{7}\rceil = 3$, but my calculator returns an…
Red Book 1
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Proving the Riemann Hypothesis and Impact on Cryptography

I was talking with a friend last night, and she raised the topic of the Clay Millennium Prize problems. I mentioned that my "favorite" problem is the Riemann Hypothesis; I explained what it posits and mentioned that, if proven, it would have great…
apnorton
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RSA in plain English

I'm a computer science student, I'm not a mathematician, I don't know anything about number or group theory. I'm looking at RSA, and I want to understand it. I know what Fermats's little theorem and Euler's totient function are, and this is what…
nkint
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good books on Abstract Algebra and Cryptography for self-study

I want to self-study some abstract algebra and cryptography during the summer, so what are some of books that are suitable for self-study? I have very limited background in algebra and none in cryptography, and like to learn by examples. Also,…
user8969
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Why does (1/3) mod 3016 = 2011?

So I am taking a class where we are working on a cryptography section. Basically, the course says that: $$\frac 1 3 \mod(3016) = 2011$$ or when run through Python - modified with SciPi: $$\frac 1 3 \,\%\, 3016 = 2011$$ I don't understand how or…
Zack
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RSA: How Euler's Theorem is used?

I'm trying to understand the working of RSA algorithm. I am getting confused in the decryption part. I'm assuming $$n = pq$$ $$m = \phi(n) = (p - 1)(q - 1)$$ E is the encryption key $\gcd(\phi(n), E) = 1$ D is the decryption key, and $DE = 1 \mod…
sauravrt
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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
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Homomorphic Compression

Can there be an algorithm such that, given plaintext data P,Q, and compression function e, Such that if we treat P and Q as a number (a series of bits): $$\begin{eqnarray*}e(P + Q)& =& e(P) + e(Q)\\ e(P*Q) &=&…
Sidharth Ghoshal
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Finite field, I don't quite understand the concept

What is the concept behind AES's finite field? I understand most of you will laugh at my lack of understanding of the concept. I'm trying to learn a greater amount of higher math concepts and I am implementing AES to do so. I understand that in a…
Will03uk
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Are there practical applications to the new prime pair proof?

I've recently heard that its been proven that the set of prime pairs that are separated by no more than 70,000,000 is infinite. Does this have any impact on cryptography or another practical application?
AncientSwordRage
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