Questions tagged [cryptography]
Questions on the mathematics behind cryptography, cryptanalysis, encryption and decryption, and the making and breaking of codes and ciphers.
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Conway Polynomial for p=2, n=3?
Im doing an exercise on Conway polynomials. As far as im concerned, for p=2, n=3 both
$f(x)=x^3 + x^2 + 1$
and
$g(x)=x^3 + x + 1$
satisfy every condition. According to every source i found, the latter ...
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How can I be certain of the existence of elliptic curves of certain order when the parameter a is fixed?
My question came up while researching an attack on Elliptic Curve Cryptography (described in Computer Security - ESORICS 2015.
I'm given an elliptic curve $E$ defined by $y^2=x^3+ax+b$ over the finite ...
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Determine Whether a Pseudorandom Generator Is Secure
Let $G: \{0, 1\}^s \to \{ 0, 1\}^n$ be a secure pseudorandom number generator (with $s$ seed bits and $n$ output bits).
I have attached a problem below that I am confused about; Which generator $G'$ ...
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Problems about Probability Analysis of the Success Rate
I am currently reading a paper on linear cryptanalysis and I am a bit confused by the probability analysis of its success rate. I wonder if I can seek advice here?
Let $N$ be the number of given ...
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distribution of square roots of unity $mod n$ | Factoring with inverse pair
I am writing a proof related to the RSA cryptosystem, specifically showing that given an inverse pair $d, c$ under multiplication mod $\phi(N)$, where
$$ dc \equiv 1 \pmod{\phi(N)}, $$
there exists a ...
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Proof of Golomb's three randomness postulates for binary sequences [closed]
I want to prove that the binary sequence generated by a max-length linear feedback shift register (LFSR) satisfies Golomb's balance, run and autocorrelation postulates:
The numbers of zeros and ones ...
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$\epsilon$-secure encryption system
Suppose the message space of a symmetric key encryption system is infinite (countable) with a probability distribution on it such that { $m \in M: Pr(m) \neq 0$ } is infinite. For a real number $\...
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Confusion on the procedure of public-key and private-key cryptography
Procedure: $1):$ choose two distinct primes $p$ and $q$.
$2):$ calculate $n=pq.$
$3):$ compute $\phi(n)=T$.
$4):$ get $E$ from $gcd(E,T)=1.$
$5):$ get $D$ from $ED \equiv 1 \pmod{T}$
To encrypt the ...
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Shortest vector problem as hidden subgroup problem
I posted this question on the cryptography stack exchange with a bounty, but I haven’t gotten much attention. I think part of the reason might be that I’m really interested in the use of group theory ...
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Root finding of multivariate polynomials over the integers
TL;DR: is there any library for multivariate polynomial root finding over the integers?
I'm trying to implement an attack on RSA with known bits of p by using Coppersmith, such as shown in this paper. ...
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How do I solve a discrete log using pen paper for exam without bruteforcing it? [closed]
I have my Network Security finals. In elgamal cryptosystem, I am often encountering these equations like this
3 = (10^XA) mod 19
now everywhere I am finding only ...
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Analyze the probability distribution of a specific sequence $S(x)$ with compensation mechanism
I'm developing a theoretical model for a sequence $S(x)$ equally spaced in the time dimension where each element is randomly preselected from set $\{1,2,...,L\}$, but the real selection(when it's turn)...
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Embedding degree of an elliptic curve
I've been reading about the embedding degree of elliptic curves in Costello's "Pairings for Beginners". The following equivalent conditions are given for the embedding degree (p51):
where $...
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Can we do any better bijective mapping of a permutation series which is only bijective for a probabilistic subset of its input domain?
So we want to bijectively map one path to another. But depending on start and target node we can only choose from a subset of all transitions. It would look like this:
We also do not know where one ...
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RSA finding D key
Given the RSA public key find the decryption key d and decrypt the ciphertext c=5.
Known information:
n=221, p=17, q=13, e=11
$\phi(n) = (p-1)(q-1) = 16\times 12=192$
Equation for finding d:
$$ed\...
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