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
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RSA signature scheme-Find a valid signature

Construct a pair of private/public key RSA, where the prime numbers that we use are $p=11, q=13$. Describe how we can calculate a RSA signature at the message $m=2$ without using a hash function. Show that, given the above signature, we can…
Mary Star
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ElGamal signature scheme

Alice uses the ElGamal signature scheme in the group $(\mathbb{Z}/p\mathbb{Z})^{\star}$ without the use of a hash function. To sign the message $m \in (\mathbb{Z}/p\mathbb{Z})^{\star}$ she calculates the signature $(r,s)$ as follows: she choose a…
Mary Star
  • 13,956
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Apply Pohling-Hellman to calculate the discrete logarithm

I am looking at the following example of calculating the discrete logarithm with Pohli-Hellman. The group is $\mathbb{F}_{29}^{\times}$ and we given $y=10$ and $g=3$. We want to find $0 \leq x \leq 28$ such that $y=g^x \pmod {29}$. I have done the…
Mary Star
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cryptographic hash functions

Suppose $ℎ: \to $ is a hash function. For any $\in $ , let $ℎ^{−1}()=\{:ℎ()=\}$ and denote $=|ℎ^{−1}()|$. Define $=|\{\{_1,_2\}:ℎ(_1)=ℎ(_2)\}|$. Note that N counts the number of unordered pairs in X that collide under h. a) Prove that $\sum_{y\in Y}…
sena şaşmaz
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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 sender and receiver have their own encryptors and…
e.ahmed
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Fermat Factorization

Does anyone know how I can use Fermat Factorization to find the two prime factors of the integer $n = pq = 321179$? I am not sure how to go about solving this and any help would be much appreciated!
John
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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?
The Doctor
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Help with linear recurrence.

I am trying to understand the following problem: Consider the following linear recurrence over $Z_2$ of degree four: $z_{i+4} = (z_{i+3} + z_{i+2} + z_{i+1} + z_{i}) \bmod 2$ i >= 0. For each of the 16 possible initialization vectors …
Connor
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Function for encryption/decryption - What is $n \phi(n)$?

In my notes there are the following functions of encryption/decryption: $$E_k(x)=x+k$$ $$D_k(y)=y-k$$ ($E_k : \mathbb{Z}_n \rightarrow \mathbb{Z}_n$) ($D_k : \mathbb{Z}_n \rightarrow \mathbb{Z}_n$) $$E_k(x)=ax+b, a\in \mathbb{Z}_n^{\star} , b…
Mary Star
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Decrypting an Affine Cipher with Modulus

I'm trying to decrypt the ciphertext vczkh which I know was encoded using an affine cipher with the equation 7x + 8(mod 26). This makes my decryption function p = (c – b) * a^-1 (mod 26) where b = 8, a = 7, c = number corresponding with cipher…
Nick Gilbert
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Factors of the RSA modulus

In the article "A Method for Obtaining Digital Signatures and Public-Key Cryptosystems", the original RSA article, it is mentioned that Miller has shown that n (the modulus) can be factored using any multiple of φ(n). Imagine I know the public and…
user3343768
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RSA decryption where e=3 m=12

I have a problem with RSA Decryption, if I set $n=3*11=33$ I get $\varphi(33)=20$ and e=3 the first problem is encrypting the Message 12, when I encrypt $12^3\equiv 12 (mod 33)$ meaning the the encryption is also 12 the second problem is when I…
user3453625
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Undoing anonymous donations

All the students in a class are planning to do a trip. Not all of the students can afford it, and it is considered shameful to reveal their poverty. So it is suggested that anyone can donate anonymously to a fund. If the fund becomes big enough to…
Jostein Trondal
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Find a polynomial of degree $8$ with integer coefficients with given root

algorithm to find a polynomial $f(x)$ s.t (1) $degree(f(x))<9$ (2) Integer coefficients (3) Absolute value of coefficients $< 10^5$ (4) f(39.770525) =~ 0 about to be <<10^-10 I heard that it is similar to coppersmith algorithm, but I can't find…
Kevin
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Trouble Understanding Pinocchio (Verifiable Computing) Sparse Polynomials

I hope I'm asking the question properly. I've never asked anything on this exchange before, but I didn't know where else to ask. The paper in question I've almost got all the pieces to understand can be found here…
psycotica0
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