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

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0answers
14 views

Encode/decode hexadecimal challenge [on hold]

So there is or was a sponsored challenge about encode/decode hexadecimal. Why does X becomes Y and is it possible to reverse Y without X? ...
1
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0answers
13 views

Example of using the Hadamard's matrix to determine the superposition

I've came across those notes for Quantum computation from John Watrous. I am having troubles understanding the last example. We have those two vectors, or if I understood correctly, from now on ...
5
votes
3answers
124 views

Factoring product of two primes from solutions of congruence

The algorithm purposed to play a fair game of heads or tails over the phone given here claims that knowing the four solutions to $$ x^2 \equiv a^2 \pmod n$$ would allow us to factor $n$ where $n$ is ...
1
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0answers
20 views

Isomorphic encryption or homomorphic encryption?

Many encryption functions are said to be homomorphic: http://en.wikipedia.org/wiki/Homomorphic_encryption As encryption functions are invertible, they can be considered one-to-one and onto on ...
0
votes
1answer
31 views

Diffie Hellman: Subgroup Confinement Attack

how can I solve the following tasks? a) Find all primitive elements of $\mathbb{Z}_{37}$. I guess the only possibility here is to try if the remainder off all elements from 1 to 36 to the power ...
1
vote
1answer
34 views

Generator of the unit group

I am required to find a generator of the unit group of $\mathbb{F}_{125}=\mathbb{F}_5[x]/(p(x))$, where $p(x)\in\mathbb{F}_5[x]$ is the irreducible polynomial $p(x)=x^3+x+1$. Does someone know how to ...
-1
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1answer
54 views

How is matrix used in cryptography [closed]

In my first lecture of matrix my teacher had said that matrix finds use in cryptography. But I would want to know how exactly is the concept of inverse and transpose etc is used in cryptography. I ...
0
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1answer
12 views

Hil 2-cipher with 26 letter alphabet

A Hil 2-cipher with a 26-letter alphabet $A=1, B=2, \dots, Y=25, Z=0$ has enciphering matrix $A = \begin{bmatrix}19 & 13 \\ 6 & 3\end{bmatrix}$ Questions Verify that $A$ is ...
2
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1answer
31 views

RSA, cipher, Cryptosystem

I genuinely have no idea how to go about solving this, any hints would be helpful
0
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1answer
23 views

Digital Signatures using RSA

RSA can be used for digital signatures this way: B creates $m$ (product of two primes), $r$ (a number for what gcd($r$, $\Phi(m)$ equals 1) and tells $m$ and $r$ A. B chooses $s$ which is the ...
1
vote
1answer
37 views

modulo RSA decrypt question

Given the following RSA generated public key: $P(3, 55)$. Which integer value should be chosen for $d$ to decrypt messages encrypted with $P$? Check your answer with $M = 8$ and $C = 17$. ...
2
votes
1answer
38 views

RSA cryptography?

I understand how RSA cryptosystem works; however, I am not sure how to apply it to answer these questions. Can someone explain please? Let $N=3869$ and be equal to the product of two distinct, ...
1
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0answers
19 views

cryptographic hash functions

Suppose $β„Ž: 𝑋\to π‘Œ$ is a hash function. For any $𝑦\in π‘Œ$ , let $β„Ž^{βˆ’1}(𝑦)=\{π‘₯:β„Ž(π‘₯)=𝑦\}$ and denote $𝑠𝑦=|β„Ž^{βˆ’1}(𝑦)|$. Define $𝑁=|\{\{π‘₯_1,π‘₯_2\}:β„Ž(π‘₯_1)=β„Ž(π‘₯_2)\}|$. Note that N counts the ...
1
vote
0answers
15 views

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 ...
0
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1answer
23 views

Question involving DES cryptosystem

This is probably an easy question. Im Assuming whoever can answer this has access to S-boxes and P boxes etc. Suppose the input to a round of DES is $1010101010......10101010$. (64 bits) Suppose ...
0
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0answers
13 views

Torelli Shanks Algorithm - Repeated Squarring Method

This algorithm is using when you want to find a square root of a number in a given moduli. I can't see the idea behind this algorithm, so can someone explain it in a simple way?
2
votes
1answer
48 views

How do I find nine messages which are unchanged by RSA encryption using the public key $(3869, 3)$.

I understand how RSA crytosystem works, however I am not sure how to apply it to answer these questions. Can someone explain please? Let $N=3869$ and be the product of two distinct unknown odd prime ...
2
votes
1answer
38 views

Topics in elliptic curves over finite fields

First of all, sorry if I didn't put this question in the correct category. This a paper aimed for undergraduate math majors. So I am writing a general paper explaining about elliptic curves over ...
0
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0answers
15 views

Problem with DES Encryption

If the input string to a round of DES is 11001100 Β· Β· Β· 1100 = β€˜1100 Γ— 16β€² and if the round key is 1111 . . . 111 (β€˜1 Γ— 48β€²), Then how can I calculate the 20th and 33rd output bits ? This was an ...
2
votes
0answers
16 views

question based RSA Algorithm

The RSA system was used to encrypt the message M into the cipher-text C = 6. The public key is given by n = p q = 187 and e = 107. In the following, we will try to crack the system and to determine ...
1
vote
1answer
26 views

What are some good resources to study Cryptography?

What are some good resources to study Cryptography? I have knowledge of abstract algebra .Is it enough to take up Cryptography as a special paper or I will have to undergo courses in some other ...
0
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0answers
21 views

Decryption of RSA

I am given the following information about an RSA-encryption: $e=31671865305320609$ (public key) and $n=10e+3$. Then I am given the ciphertext $c$ which I omit here due to his length. The task is to ...
0
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1answer
26 views

Math behind perfect hash

I am reading material on cryptographic hash functions and it says "Collision resistant property : for a hash of length L, a perfect hash would take $2^{L/2}$ attempts." Can someone explain why? ...
0
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0answers
11 views

asymmetric cipher with multiple public keys [migrated]

asymmetric cryptography is well known. You generate private key. Using private key you generate public key. Then you can sign a message with private key and check signature using public key. I need ...
0
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0answers
27 views

How to decrypt a ciphertext by using the mutual index of coincidence?

I am trying to decrypt a VigenΓ©re cipher text. I have found the key length by computing Index of Coincidence of substrings. The key length is 12. I know the letter frequencies the string and the ...
18
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3answers
4k views

Why does (1/3) mod 3016 = 2011?

So I am taking a class where we are working on a cryptography section. Basically, the course says that: $$\frac 1 3 \mod(3016) = 2011$$ or when run through Python - modified with SciPi: $$\frac 1 3 ...
1
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1answer
36 views

How is de = 1 (mod Ο•(n)) calculated

I am reading RSA algorithm. So, I was writing a question but I saw this question and still couldn't understand it. If $$e\cdot d \equiv 1 \pmod{\varphi(n)},$$ then $$ed=k\cdot \varphi(n)+1, \qquad ...
1
vote
2answers
21 views

Proof DES is injective - is this a valid argument

Without going too much into detail into the crpytography of the matter since not every mathematician is interested or knowledgable in the field, there is an encryption process called DES (data ...
0
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0answers
13 views

What is the proper way to generate a key in Merkle-Hellman Knapshack Cryptosystem?

This article says that, if a message is 8-bit, then there should be 8 elements in the Super Increasing Sequence. ...
1
vote
1answer
26 views

Is it possible to estimate the number of primes between 0 and a 128 bit number?

I'm attempting to visualize an RSA public/private key pair, or a SHA2 hash. In order to reduce that massive number that is meaningful to humans I'm looking at this SHA2 visualization function to ...
72
votes
6answers
7k views

Mathematically, why was the Enigma machine so hard to crack?

Mathematically, why was the Enigma machine so hard to crack? In laymen terms, what was it exactly that made cracking the Enigma machine such a formidable task? Everything I have seen about the ...
0
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2answers
19 views

Calculating all Possible Keys vs All possible numbers confusion

With a key of length n bits, there are 2n possible keys. eg: 128-bit key length will have 2128 possible keys But when calculating every possible n digit number, ...
5
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1answer
136 views

How fast was the Turing's machine for breaking the enigma code?

We know that, recently, personal computers make around $10^9$ calculations per second, and I'm just curious about how many calculations was able to compute the machine invented by Turing for breaking ...
0
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0answers
12 views

how to calculate number of points on an Elliptic curve over prime field? suggest any best method

$y^2=x^3+a*x+b\pmod p$. For this elliptic curve over prime field, how to calculate number of points lies on the curve? suggest any best method.
0
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0answers
55 views

Solving RSA cipher without calculator

I have a question: Encrypt the message UPLOAD using RSA with $n=3\cdot 31$ and $e =17$. My question is, how can I solve this with a calculator and in an efficient manner due to being in an exam ...
0
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1answer
28 views

Why wasn't the length of key mentioned in this algebraic notation of Vigenere Cipher?

Let, $M=m_ 1 m_ 2 m_ 3 ... m_ n$ and, $K=k_ 1 k_ 2 k_ 3 ... k_ m$ Then how algebraic notations of Vigenere Cipher should be? In the following pages key-length and message-length are shown same. ...
0
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0answers
21 views

Why AES uses polynomials instead of numbers

In AES, the numbers actually represent polynomials and all operations like addition, multiplication have rules according to modular polynomial arithmetic. I don't understand the need to have ...
1
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1answer
121 views

What do these notations mean, if we read those in English?

If m: message, M: message space, k: key, K: keyspace, c: cipher, C: cipher space and $E_k$: encryption function, such that $E_k(m) = c,\ m,m^* \in M,\ k\in K,\ c\in C.$ Then, what do the following ...
3
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1answer
47 views

How can I calculate Index of Coincidence of Vigenère cipher?

I have computed the letter frequency of the cipher text. However, I don't know how to apply Friedman Test to Vigenère cipher. I couldn't calculate the Index of Coincidence. Does anyone can help to me ...
2
votes
2answers
37 views

RSA and extended euclidian algorithm

I'm learning about RSA, public private key stuff, and I just found a very nice article explaining the basics. ...
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0answers
38 views

Generator of group, Computation of discrete logarithm

The prime number $p=67$ is given. Show that $g=2$ is a generator of the group $\mathbb{Z}_p^{\star}$. Compute the discrete logarithm of $y=3$ as for the base $g$ with Shanks-algorithm. Compute the ...
1
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0answers
24 views

Given plaintext and ciphertext of the same length, how could one generate potential symmetric keys if encryption algorithm is unknown?

This question is about both encryption and about how and if one could transform data from one given form to another given form and back. I am given plaintext and ciphertext, both of which are the ...
0
votes
1answer
35 views

Exponentiation for hash function & associativity

Some cryptographic papers use $H^n(x)$ to mean $H(H^{n-1}(x))$ where $H^0(x) = x$ and $H$ is a cryptographic hash. So $H^3(x)$ would be $H(H(H(x)))$. Is this definition formally correct? It seems to ...
0
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1answer
57 views

Non-constant Linear Boolean Function

How can we prove that any non-constant linear Boolean function is balanced ? I know that any non-constant affine function is balanced. But i cannot expend this for Boolean function.
2
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1answer
62 views

Why in RSA, the public exponent $e$ must be coprime with $\phi (n)$

I'm trying to understand the RSA cryptosystem, and that's what I know so far: If we think about some number $m$ as the message, then we are searching a $e$ and $d$ such that $$m^{ed} \equiv m \ \ ...
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0answers
28 views

Latin Squares and Olderogge Code

So I have two Latin Squares, $A$ and $B$ that form a pair of MOLS of order $m$. I then have an Olderogge code formed from $A$ and $B$, where each binary vector of length $m^2$ is encoded as a codeword ...
0
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0answers
24 views

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?
0
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1answer
45 views

Basic Modular Exponentiation question

I just know this rule :ab mod n = [(a mod n)(b mod n)] mod n. How can it be proved that the following rule is true ? ...
3
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0answers
33 views

Shamir's secret sharing interpolation problem

I try to understand this protocol - Shamir's secret sharing - threshold scheme. I got my data and I made interpolation basing on examples published on Wikipedia. You can see them below (sorry, I am ...
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1answer
15 views

Determine a positive integer $e$ that satisfies $M^{17e}\equiv_{77}M$, when $(M,77)=1$.

We're doing public key cryptography this week and I just can't seem to get a grasp on it. I really don't know how to solve this problem. Can anyone point me in the right direction? I'd really ...