Questions on cryptography and cryptanalysis, encryption and decryption, and the making and breaking of codes and ciphers.

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3
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1answer
65 views

Permutations: If I know $\alpha$ and the cycle structure of $\alpha\beta$, can I find $\gamma$ for which $\gamma\beta$ also has this cycle structure?

Suppose we have two permutations $\alpha$ and $\beta$ (of a set $S$ of size $|S|=n$), and I know $\alpha$ and the cycle structure of $\alpha\beta$. But I don't know $\beta$. Can I find a ...
2
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1answer
43 views

Is there a cipher that yields two separate but valid results depending on the key?

Suppose the following. Someone wishes to encrypt a message so it is not intercepted. With traditional ciphers, if the key is guessed correctly, the message is revealed. This cipher is similar– ...
2
votes
1answer
35 views

Solve for a variable in mod

I want to solve for $s=\frac{(M-x^y)}{r}$ mod $(p-1)$ where I know the values for $M,x,y,p,s$ but don't know $r$. How can I solve for $r$? I tried to solve for $r$ by trying to compute ...
1
vote
1answer
43 views

Relation of encryption to P, NP, and NP-Complete

After watching a Harvard Lecture regarding the understanding of P, NP, and NP-Complete,they also talk about our encryption algorithms being cracked or useless once we solve the mathematics side of it? ...
1
vote
1answer
107 views

RSA Ciphertext Message.

Hey I'm really stuck and I have to finish soon. Part A Ray, Sam and Todd are lazy, and they have set up their RSA public keys as $(3,nR),(3,nS),(3,nT)$ respectively. We may assume that any two of ...
1
vote
1answer
64 views

El-Gamal: Recovering random number r

For a padded message, M, using the El Gamal encryption schema, how can we determine the random number $r$, when we are given $p$, the prime number, $g$ which is the primitive root of $p$, $b$ and $x$ ...
1
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1answer
36 views

One-way functions and pseudorandom number generator

Is it true that if there is Cryptographically secure pseudorandom number generator then there is One-way function?
1
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1answer
79 views

Diffie-Hellman key exchange for three user.

Assume that there are three users that have their own secret key $d_i$ and corresponding public key $Q_i = d_i G$ such that $Q_i$ is a point in an elliptic curve. Now I'm looking for a solution to ...
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0answers
14 views

What is an embedding degree of elliptic curve?

I am dealing with MOV algorithm to transform ECDLP to DLP in $GF(p^k)$, but at the first step I have to determine embedding degree k. I have read the definitions of embedding degree, but still I am ...
0
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0answers
24 views

Studying a code in cryptography

So,i'm given a binary code $C$ with it's generator matrix $G=(A,B)$ where $A,B$ are given matrices. The task is to study the code. First question: What does this form $(A,B)$ mean? how would $G$ look ...
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0answers
46 views

Factor a big number by Pollard Rho method

How to factor $2^{2^8}+1$ by Pollard Rho algorithm? I have tried this question,but I have no clue. In order to use Pollard Rho, I should know some factor of this number right? But how can I find one?
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19 views

How is the table generated for Galois Field?

If I want to generate tables for $01AB\quad 01AB$ for both addition and multiplication, how will it be generated? I am basically confused from this wikipedia example! I hope someone can clear it up ...
0
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0answers
15 views

How to do Rijndael MixColumns step

I am trying to go through all of the the steps in the Rijndael Encryption Algorithm using pencil and paper. I have been using ...
0
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0answers
41 views

Probability theory in (classical) cryptography

In (classical) cryptography we have the formal definition of a cryptosystem that is a quintuple $(M,C,K,e,d)$ where $M$ is the (finite) set of plaintexts, $C$ is the (finite) set of ciphertexts, $K$ ...
0
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0answers
15 views

How to determine sub-exponential time growth?

I'm a little bit confused of sub-exponential time growth; consider the definition from Hoffstein's book An Introduction to Mathematical Cryptography: Given input of $k$ bits, then if an algorithm ...
0
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0answers
47 views

RSA Decryption - finding Private Key

Let p and q be primes and $e \in \mathbb{Z}^+$, with $\gcd (e, (p-1)(q-1)) = 1$. Let d be the inverse of $e \mod (p-1)(q-1)$. The decrption process where M is plaintext and C is ciphetext ...
0
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0answers
33 views

DLP in a Cyclic group

Let q be a prime. G is a cyclic group of order $q^2$. Show that for solving the DLP in G it's enough to solve two distinct DLPs in two groups of order q . --- We are looking for an x such that ...
0
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0answers
26 views

Infinite One-Time Pad

As you know, when used correctly, a one-time pad allows one to send a message, such that the only thing that can be found out about it is the maximum size (which is also the key length.) It is ...
0
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0answers
23 views

Provide sample matrices that could be keys in the Hill cypher

Well, to encrypt some message I need to multiply parts of it by some matrix key, and to decypher it I need to multiply the output by the inverse matrix. But I've found an excercise to provide some ...
0
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0answers
38 views

enumerating in pseudo random order - version 2

edit 2: what kind of statistical test do I need to get an idea of the randomness of the order of a list? The list contains all base-4 numbers from 0000 to 3333 exactly once. edit 1: I've added ...
0
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0answers
32 views

Diffie-Hellman key exchange problem

I would like to ask about a little help about a Diffie Hellman key exchange problem with polynomials. Until now i've solved such problems with numbers, so the algorithm is clear for me. The confusing ...
0
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0answers
46 views

Using knapsack problem for digital signatures

Is it possible to use the knapsack problem for digital signatures? What I am imagining is something like the Merkle–Hellman knapsack cryptosystem, but used for digital signing, rather than encryption. ...
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0answers
194 views

Why does RSA have to use Euler's Totient function?

$$\begin{aligned}m^{ed} &\equiv m\bmod n\\ ed &\equiv 1 \bmod \phi(n)\\ \end{aligned}$$ Why does the modulus of the modular multiplicative inverse have to be the totient function? Won't any ...
0
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0answers
37 views

Insecure second preimage problem for polynomial hash

Define a compression function $h: \mathbb Z_{2^n} \to \mathbb Z_{2^m}$ (so $n>m$) by: $h(x) = \sum_{i=0}^d a_i x^i \mod \mathbb Z_{2^m}$ where $a_i \in > \mathbb Z$ and $0 \leq i \leq ...
0
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0answers
44 views

How to determine if an array of digits is random?

Array1: 9999999999... This is not random because its significant deviation from a uniform distribution Array2: 12345678901234567890... This is not random because the distance between two nearest ...
0
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0answers
19 views

How do I graphically visualze a multi-party scenario with at least 4 different variables?

How can I view the below scenario graphically using the variables $M$,$n$,$k$,$epsilon$ in a way that makes sense? I have $n$ parties that I want to divide up in $k$ bins (or committees). Each party ...
0
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0answers
10 views

What is the name of the specific kind of involution used in most reciprocal ciphers?

Is there a name for the subset of involution functions used in most reciprocal ciphers? I've been saying things like A pairing is a function f that pairs up each element x with some other element y, ...
0
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0answers
48 views

how to encrypt “STACK” using RSA with keys $e=133,n=2160$

$n=2257=37\times 61,\phi(n)=2160$ A B C D E F G H I J K $\space $L$\space $ M$\space $ N$\space $ O$\space $ P$\space $ Q$\space $ R $\space $S$\space $ T $\space $U $\space $V$\space $ ...
0
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0answers
59 views

If $n$ is a Carmichael number then there exist at least one $a: a^{(n-1)/k} \equiv 1$ (mod n)

If $n$ is a Carmichael number then there exist at least one $a: a^{(n-1)/x} \equiv 1$ (mod n) such that $a^{n-1} \equiv 1$ (mod $n$) and x is prime such as $x |(n-1)$. I am solving the bigger proof ...
0
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0answers
43 views

$c$ primitive root, $a \in \{1,\ldots,p-1\}, w/ j \in \mathbb Z^+, a \equiv c^j \pmod p), a^{\frac{p-1}{2}} \equiv 1 \pmod p\implies j\text{ even}$.

Suppose c is a primitive root modulo $p$. Suppose you have a particular integer $a \in \{1,2,\ldots,p-1\}$ and you have found $j \in \mathbb Z^+$ such that $a \equiv c^j\pmod p$. Show that if ...
0
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0answers
46 views

Must the “n” in mod(n) always be prime?

I'm experimenting with mod(n) and have the following questions even after reading the Wiki page and numerous articles about the subject. Must mod(n) always be prime for cryptographic purposes? Is ...
0
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0answers
20 views

Why do the authors claim f(u) does not reveal anything about the random subspace X?

On pg. 8 under section 2.1 (Random Subspaces are Leakage Resilient) the authors claim "In the latter pair, the leakage function reveals nothing about the subspace X, and therefore we conclude ...
0
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0answers
19 views

Search Space Function:

given a set of integers: ${x_1, x_2, ... x_n}$ Is is possible to construct a generic function $f$ such that there exists $u_1 .... u_n \in R$ where $f(u_k) = x_k$ and: $$f(x+y) = f(x) + f(y)$$ ...
0
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0answers
24 views

how does this informal proof show a particular PKE scheme is secure against non-adaptive memory attacks?

On pg. 5 of this paper the author does a section on the "Idea of the proof" using a technique known as dimension reduction. The actual proof is on pg. 13 Section 3.1 of the same paper. However, I am ...
0
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0answers
50 views

Hash functions that produce a point on an elliptic curve.

I see in some cryptographic papers, that the authers of those papers utilize of a hash function such that that hash function converts an integer value or octet-string value as input, to a point on an ...
0
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0answers
58 views

Addition a point on an elliptic curve with an integer value

Suppose $Q$ is a point in an elliptic curve such that $Q=dP$ and $d$ is an integer value, and $P$ is base point of that elliptic curve. Note $Q = dP$ means that $P+\cdots+P$ for $d$ times** and since ...
0
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0answers
45 views

Show that we can use d' for the decrypting exponent, where d' is a solution of ex=1 (mod lema(m)).

Let $p, q$ be distinct odd primes and let $m' = \text{lcm}(p-1, q-1)$, the least common multiple of $p-1$ and $q-1$. Suppose we set up an RSA cryptosystem with a modulus $m = pq$ and an encrypting ...
0
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0answers
81 views

Is Hash(bG) equal to b(Hash(G))?

Assume b is an integer, G is a basepoint in an elliptic curve, and Hash is a one-way hash function. Is Hash(bG) equal to b(Hash(G)) ? or not? Note: A hash function is any algorithm or subroutine ...
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0answers
50 views

Formula for checking the probability of a character appearing multiple times consecutively in an encrypted string

I am a young CS student with a specific interest in Cryptography, but I am relatively new to the field. Yesterday I came across a question I could not answer by myself, so I thought I'd ask some more ...
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0answers
74 views

How to calculate RSA Cryptography for small prime numbers?

Probably duplicate of Why are very large prime numbers important in cryptography? But my question is,what if we start with two small prime numbers say $p = 3$, $q = 5$ and $n = pq = 15$, $\phi(n) = ...
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0answers
80 views

How would I create a birthday attack? (Hash Functions)

I'm trying to create an birthday attack, but I can't seem to get through it as I've never done it before. The basis: We have $E_K$, an encryption function, which has $N$ possible keys $K$, $N$ ...
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0answers
46 views

Can someone explain this equation?

Okay, here is the exact phrasing: We want to get two values $A$ and $B$, where we test many values of $A$ to get the smallest value of $B$. $B$ is the coefficient of $x^{15}$ in the result of: $(1 + ...
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0answers
26 views

If the plaintext is “HELPMEAR” and the block size is 5, determine the key

We first add on 2 random characters XX to the end to make the number of characters equal to 10. So we get: HELPMEARXX which we can seperate into. (I think) XXRAE MPLEH So the key should be 2 ...
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0answers
77 views

Markov Chain and cryptanalysis

Where I will be able to found papers to read the state-art of the use that Markov chain in cryptanalysis. I founded this Canteaut, A. and Chabaud, F. (1998). A new algorithm for finding ...
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0answers
25 views

Computing discret logarithm $log_{g}(h)$ such that $g,h$ are generators for the cyclic group $Z^{*}_{p}$

Let $p$ be a prime number, $g, h$ be generators of the cyclic group $Z^{*}_{p}$ , and $f$ be defined as: $f : \lbrace 1, . . . , p − 1\rbrace^{2} → Z^{∗}_{p}; (x,y) \rightarrow g^{x}h^{y}\;mod\;p$. ...
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0answers
158 views

homomorphic encryption

Homomorphic encryption is a form of encryption where a specific algebraic operation performed on the plaintext is equivalent to another (possibly different) algebraic operation performed on the ...
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0answers
181 views

Cryptoanalysis of RSA

I am having trouble with this problem: Suppose that you would like to use the RSA system to send the secret message $P$ to a colleague across an insecure line of communication. Assume that you ...
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0answers
74 views

entropy of perfect cryptosystems

I am working on the product of two perfect crypto-systems and I need to prove that the product is secure. $$a -- [\text{system}\ 1] -- b -- [\text{system}\ 2] -- c$$ How can I prove that $H(a) = ...
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0answers
396 views

Index Calculus for Discrete Logarithm Problem

I am trying to implement index calculus algorithm for discrete logarithm problem. In general the algorithm works like this : Input: Zp, order d, generator a, b element of Z Output: log_ab 1- find a ...
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22 views

What is Attribute-Based Encryption?

Can someone kindly guide me from where can I get some simple explanation about attribute-based encryption i.e. aside from the scientific papers? I was searching for a book or something that can help ...