All Questions
Tagged with cryptography combinatorics
36
questions
-1
votes
1
answer
140
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Intersecting solutions
The following problem is one of those I give to my students as a homework trying to test their combinatorial skills. It is one of those technically routine "intermediate" statements one has ...
- 1,773
0
votes
0
answers
101
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How easy is it to break this encryption system a buddy of mine and I just discovered?
This is gonna take a little bit of background to explain, so here goes:
In base $11$, we have $11$ numerals to form numbers: $0, 1, 2, 3, 4, 5, 6, 7, 8, 9$, and since there is no single symbol ...
- 6,833
0
votes
2
answers
162
views
What is the formula for determining how many errors a generator matrix can correct?
I am wondering whether or not there is a generic formula for determining how many errors a generator matrix is able to correct if also provided the field the code is in. For example, given the ...
- 313
2
votes
1
answer
67
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Principle of Inclusion-Exclusion with Substitution Ciphers
Consider an alphabet with $2n$ symbols and the substitution cipher that maps $p_i$ to $c_i$ for all $i$. If the numerical representation of $p_i = i$ for every $i$, how many substitution ciphers exist ...
4
votes
1
answer
157
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Is derivative a one way function?
In lectures we have just defined integrals, and said that if we take a derivative of some set of functions, it is much harder to go back to the original set of functions, if we only know the set of ...
- 2,527
2
votes
2
answers
64
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Why is this seemingly more-restricted set of possible passwords larger than this less-restricted set?
I'm doing a password cracking challenge right now, and I know several restrictions of the password.
The password is 8 characters long
The first character is a lowercase letter, the second character ...
- 33
0
votes
1
answer
135
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Decrypting the Vigenere cipher ACTMEFPTQBFPLZRDPTQBFH
After finding all the bigrams, I concluded the key length has to be either 5 or 10, In the case of 5, the index of coincidence is a 0, while for 10 it's 1/225.
Which 1 is more likely to be the key? ...
- 53
2
votes
3
answers
62
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How can I increase the complexity of a number and maintain uniqueness
I have an 8-digit number and you have an 8-digit number - I want to see if our numbers are the same without either of us passing the other our actual number. Hashing the numbers is the obvious ...
0
votes
1
answer
329
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The indicator of a Boolean function
In the paper "Componentwise APNness, Walsh uniformity of APN functions and cyclic difference sets" by Claude Carlet, it is written that: Let F be any power function on $F_{2^n}$ and $\Delta _{F}=\{F(x)...
- 77
0
votes
1
answer
66
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Proof of construction of a matrix
I have a matrix $A=\begin{bmatrix}r_{11}& r_{21} &r_{31}&r_{41}\\
r_{12}&r_{22}&r_{32}&r_{42}\\
r_{13}&r_{23}&r_{33}&r_{43}\end{bmatrix}$, As we see that taking ...
- 2,632
1
vote
1
answer
416
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Dual of generalized Reed-Solomon code
I need to show that $GRS_{n,k}(\alpha,\mathbb{1})^{\perp}=GRS_{n,n-k}(\alpha,\alpha)$, where $\alpha=(1,a,\ldots,a^{n-1})$, $a$ is a primitive $n$-th root of unity, $\mathbb{1}=(1,1,\ldots,1)$.
So, ...
- 941
10
votes
3
answers
1k
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Secret Santa algorithm that does not rely on a trusted 3rd party?
With a trusted 3rd party, running Secret Santa is easy: The 3rd party labels each person $1,\dotsc,n$, and then randomly chooses a derangement from among all possible derangements of $n$ numbers. ...
- 404
0
votes
1
answer
354
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Birthday attacks vs. Preimage attacks
I am trying to understand why a preimage attack is different than a birthday attack.
Following the general description from Wikipedia (sorry if that is a poor source?):
A preimage attack is where an ...
- 15
3
votes
2
answers
158
views
Hamming Distance
I have a another question about calculating the size of a subset of codes.
$n := 2^q$ for a natural number $q$
$d_H(v,w) := \left| \{ i \in \{1,\ldots,n\} \; | \; v_i \neq w_i\}\right|$ for
$v:=(v_1,...
- 43
5
votes
1
answer
201
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Simple upper bound on the probability that the sum of $n$ dices rolls is equal to the most likely total
Suppose $n$ $s$-sided (and fair) dice and are rolled, and consider the most likely value their total will take. Is there a simple / easy to state upper-bound on the probability that this total is ...
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