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
50 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
21 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
votes
1answer
26 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 ...
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0answers
15 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?
3
votes
3answers
407 views

How do you determine if an elliptic curve over a finite field is cyclic?

I know the group order and the points of the elliptic curve $y^2 = x^3 + Ax + B$, but I am confused on how to determine if they from a cyclic group The curve $y^2 = x^3 + 2x +2$ in $\Bbb F_{11}$ ...
0
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0answers
125 views

RSA and El Gamal Algorithms

I have to write a short report about RSA and El Gamal algorithms in cryptography. I just need to summarize them (how one would calculate the various components, what their strengths and weaknesses ...
2
votes
1answer
50 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
46 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
18 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
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0answers
20 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 ...
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votes
4answers
11k views

Example for Cyclic Groups and Selecting a generator

In Cryptography, I find it commonly mentioned: Let G be cyclic group of Prime order q and with a generator g. Can you please exemplify this with a trivial example please! Thanks.
1
vote
1answer
34 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
votes
0answers
23 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 ...
71
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 ...
18
votes
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 ...
0
votes
1answer
32 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
32 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 ...
3
votes
1answer
54 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 ...
1
vote
1answer
85 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
19 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. ...
0
votes
2answers
24 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, ...
1
vote
1answer
31 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 ...
0
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0answers
25 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.
5
votes
1answer
149 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
votes
0answers
63 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 ...
1
vote
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 ...
0
votes
1answer
31 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
votes
0answers
22 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 ...
2
votes
2answers
44 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
43 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 ...
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vote
0answers
36 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 ...
11
votes
3answers
20k views

How to break XOR cipher with repeating key?

I need to crack a stream cipher with a repeating key. The length of the key is definitely 16. Each key can be any of the characters numbered 32-126 in ASCII. The algorithm goes like this: Let's say ...
0
votes
1answer
40 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
59 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
votes
1answer
77 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
32 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
25 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
48 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 ? ...
0
votes
1answer
50 views

Discrete Log Problem

I've been given this key for an elliptic curve crypto -system: A:=4569782456273849 B:=74578265973825694738 p:=164516845864567592349187678956932587156973824569837657473 So the EC group is ...
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votes
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 ...
0
votes
1answer
24 views

Solving ANF equations

Can anyone suggest a method of solving a system of boolean equations in ANF form? Boolean equations in ANF form (Algebraic Normal Form ) are equations of the form of xor of products of boolean ...
0
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0answers
47 views

How does the factor command on the TI-89 works?

So to put my question in context, I am working on the following problem. Let $N=1291233941$. Eve's magic box tells her the following three encryption/decryption pairs for $N$: $$(1103927639, ...
0
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1answer
69 views

Breaking RSA code

I will be grateful for some tips on how to bite a task like so: I need to break a RSA code. I know that public key is $n=462257, e=13$. I also have cryptogram $c=139552$. The goal is to find a number ...
4
votes
1answer
105 views

How does the Enigma machine ensure that no letter is substituted for itself?

In Alan Turing: The Enigma Andrew Hodges describes how the letter encodings performed by a German Enigma machine "would always be swappings" (original emphasis). And goes on to say that There was ...
0
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1answer
37 views

Confusion about negligible and non-negligible functions in crypthography

I am learning basic cryptography from Coursera's cryptography I course and am a bit confused about the negligible and non-negligible function epsilon and how it relates to the predictability of pseudo ...
0
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2answers
33 views

Exponentiation in Modular Arithmetic

I feel like this is a fairly straightforward question, but I've been having a great deal of difficult computing one modular arithmetic expression. It's this: $9 ≑ 3^a \pmod{17}$ How does one go ...
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vote
3answers
41 views

affine cipher $ax+b \mod m$

I have an affine chipher $ax+b \mod m$ For what values $a,b$ is this an injective encryption function? From what i understand thats the case when $a$ and $m$ are coprime, so $gcd(a,m)=1$ and the ...
1
vote
1answer
53 views

Artificial Integer?

Consider a function $$ f: \Bbb{Z} \rightarrow \Bbb{Z} $$ Over the integers. Furthermore consider a number E such that there doesn't exist an integer R such that $f(R) = E$ or formally stated $$ E ...