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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.
1940 questions
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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
91
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6 answers

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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4 answers

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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43
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2 answers

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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39
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3 answers

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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32
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7 answers

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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32
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2 answers

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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24
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3 answers

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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21
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2 answers

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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19
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4 answers

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
19
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3 answers

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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18
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3 answers

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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18
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2 answers

Book recomendation for Elliptic-curve cryptography

I have already taken a course on Cryptography, The course focused mainly on the public-key cryptography based on the algebraic structure of elliptic curves over finite fields. Now, I would like to deepen this topic. I've been searching for a book…
Darío A. Gutiérrez
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16
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4 answers

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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16
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2 answers

Does the Riemann hypothesis guarantee that integer factorization is difficult?

In an exchange of comments at Is there any mathematical conjecture that is successfully applied in the real world in spite of being yet unproven?, user R.J. Etienne claims that RH guarantees that integer factorisation is difficult. I was not able…
joriki
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