All Questions
Tagged with cryptography discrete-mathematics
106
questions
-1
votes
2
answers
71
views
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 ...
- 111
1
vote
1
answer
81
views
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:
$$ed\...
- 269
0
votes
0
answers
120
views
Unexpected Result from Finite Field Calculations in GF(2^8)
I'm performing calculations within the finite field $GF(2^8)$ and I can't seem to get the expected results. This is my first time working with finite fields, so my understanding is quite basic. I ...
1
vote
1
answer
49
views
Modulo composition confusion [duplicate]
In a cryptography lecture, I have run into a equation such that
$$y_i=e(x_i)=x_i+s_i(mod2)$$ $$x_i=d(y_i)=y_i+s_i(mod2)$$ where $e()$ means encryption and $d()$means decryption in Stream ciphers.
...
user1239778
4
votes
2
answers
112
views
Confusion Over The Definition of a Transposition Cipher
In our Discrete Mathematics class, the way the textbook introduces the transposition cipher is as follows:
As
a key we use a permutation $\sigma$ of the set $\{1, 2, \ldots , m\}$ for some positive ...
- 270
1
vote
1
answer
114
views
Elliptic Curve Point Addition; two possible Lambda Solutions?
I'm trying to double the Point $P(1,17)$ on the Elliptic Curve $y^2 = x^3 + 3x + 6 \pmod {31}$.
I'm using the formulae:
$$\begin{split}
λ&=(3xp^2+a)(2yp)^{-1}\\
xr &= λ^2 - 2xp\\
yr &= λ(...
0
votes
1
answer
115
views
Discrete log over a prime
I have a prime $p$ such that $p-1=2 p_1p_2$ such that $p_1$ has $200$ digits in base $2$ and $p_2$ has 50. I want to find discrete logarithm of $a^b =c \pmod p$. That is I want to find $b$ given $a,c, ...
- 43
-1
votes
2
answers
46
views
Why is entropy of three variables equal to entropy of two variables? [closed]
For each X - messages Y - encoded messages Z - keys, next statement is true:
$ H(X,Y,Z) = H(X,Z) = H(Y,Z) $
Why is that true ?
- 47
2
votes
0
answers
81
views
Finding primitive roots including negative sign
I commonly run into the following question such that if $p$ and $q=4p+1$ are both odd primes prove that $2$ is primitve root modulo q . However , i could not prove it for other number that are given ...
user1121946
2
votes
1
answer
3k
views
R.S.A. Encryption: find $d$ if we know $n$ and $e$
If an R.S.A. system has $n=55$ and the encryption key is 13
Do I choose $p$ and $q$ as 5 and 11
so $n = 5 \times 11$
and then $\varphi(n) = (5-1) \times (11-1) = 40$
Is this the correct start? Will ...
- 65
0
votes
1
answer
98
views
encrypt problem in Discrete mathematics
Consider:
$$
e = 2^{16} + 1 = 65537
$$
$$
m = a^e \text{ (mod $p$)} \oplus b^e \text{ (mod $p$)} \oplus c^e \text{ (mod $p$)}
$$
$$
n = abc x^3 \pmod{p}
$$
a is between 1000~2000, b is between 2000~...
- 1
2
votes
2
answers
111
views
Dividing Factorial formula from book
I'm reading a book Discrete Mathmatics with Cryptographic Applications and it claims that
$\frac{n!}{k!} = (k+1)(k+2)...n$ for $k<n$. But a very simple example where $n = 3$ and $k = 2, \frac{(1)(2)...
- 23
0
votes
1
answer
463
views
I want to find primes $p$ where $p-1$ is smooth [closed]
I'm using the Pollard's $p-1$ method but for some numbers this method won't work.
For example for: $n = 436916347656251$.
$$n - 1 = 2 \times 5^{10} \times 7^5 \times 11^3$$
But Pollard's algorithm ...
4
votes
1
answer
201
views
Permuted Hamming distance
Suppose Alice wants to send a message to Bob, they agree on a $n$ letters alphabet $\Omega = \{a_1, \cdots, a_n\}$ and they both agree on a shared secret $\omega=\omega_1 \cdots \omega_m$ $\omega_i \...
- 175
2
votes
1
answer
100
views
Sequence $x\mapsto x^a$ cyclic in 3 directions: $s_0^{b^ic^jd^k}\bmod N$. How to find member $ijk$ if projection to 1D not possible due mixed factors
Summery:
Can we determine $i,j,k$ for $s_{ijk}$
$$s_{ijk} \equiv s_0^{\beta^i\gamma^j\delta^k}\mod N$$
$$N = P\cdot Q \cdot R$$
$$P = 2\cdot p \cdot p_{big} +1 $$
$$Q = 2\cdot q \cdot q_{big} +1 $$
$$...
- 77