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

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6
votes
0answers
46 views

A special case of zero-knowledge computation

This question is inspired by the disappearance of Malaysian Air 370. Let's suppose the plane crashed into the ocean. These are hotly contested waters where various countries (US, China, India, others) ...
3
votes
0answers
65 views

RSA-keys are not good?

PK := (n, e) = (1765937, 23755) SK := (n, d) = (1765937, 1734043) Can someone tell me, given these keys, what is not good about them, meaning it should not be very difficult to break it? (Except ...
3
votes
0answers
189 views

Bachelor Thesis - Galois Theory Research Topics?

I'm on the last semester of my bachelor's degree (undergrad degree) and I will be writing my thesis next semester. I have talked to a professor at my university and one of the topics he suggested was ...
3
votes
0answers
75 views

crack the key or not: generated key

Let $T \in F^{n \times n}$ , $F$ be a field Let $U_1, U_2 \in F^{n \times n}$ be randomly chosen by user 1 resp. user 2. user1 sends $U_1\cdot T$ to user2 , user2 sends $T\cdot U_2$ to user1 . ...
3
votes
0answers
62 views

Notation: “belongs to” with an R subscript

I've run into an expression: $x_i \in_R \mathbb{Z}_q$ – and I wonder what this means. An example paper is here, here's example in Wikipedia. Can anybody help me? Thanks in advance.
3
votes
0answers
65 views

Does there exist an operation like bitwise-xor over non-power-of-2 domains?

I want a function for enciphering a single letter that takes two letters as input, produces one letter as output, and has the same properties as bitwise XOR. The problem is that the range of inputs ...
2
votes
0answers
29 views

How many commutative block ciphers are there?

Let $K$ and $M$ and be two finite sets. Let $(G,\circ)$ be the group of permutations over $M$ under composition. Let a (implicitly: block) cipher with key in $K$ and message in $M$ be any application ...
2
votes
0answers
165 views

Having trouble using the Chinese Remainder Theorem to solve a system of congruences

I'm working on a difficult assignment involving cryptography, and am nearing the end (or so I think). Summed up, I need to solve a system of congruences using the Chinese Remainder theorem. Due to ...
2
votes
0answers
96 views

Homomorphic Compression

Can there be an algorithm such that: given a plaintextdata P, Q and compression function e: $$e(P + Q) = e(P) + e(Q)$$ $$e(P*Q) = e(P)*e(Q)$$ The idea is closely related to homomorphic encryption ...
2
votes
0answers
51 views

Queston concerning cracking an RSA message

I don't have a clue how to solve this exercise: Let m be an RSA modulus, g an encryption Exponent and N be a space of Messages. You know that $k^g$ is such that $k \in S \subset N$ with an S of ...
2
votes
0answers
296 views

How to reverse this bitwise AND-XOR encoding algorithm?

I have been given an "encoding" algorithm that does bitwise XOR and bitwise AND. Originally it's a C code that operates on integers with bit-shifts, but I have translated it into a simpler pseudocode ...
2
votes
0answers
77 views

has any cycle found in MD5?

We are not sure whether MD5 has fixed point or not. But since the sample space is finite, it must have cycles: $$ A →(MD5)→ B →(MD5)→ C →(MD5)→ D →(MD5)→ A $$ Has any research been done on MD5 to ...
2
votes
0answers
227 views

Extending the Diffie-Hellman protocol to multiple parties

I'm going through a Coursera cryptography class, and there appeared an interesting (and currently open) problem about extension of Diffie-Hellman protocol to multiple parties, while preserving the ...
2
votes
0answers
97 views

Decryption in the Merkle-Hellman cryptosystem

In a Merkle-Hellman cryptosystem, plaintext message units are of length $3$ over the alphabet $$ \begin{array}{cccc} ...
2
votes
0answers
56 views

Are the sets $\left\{\sum_{x \in \operatorname{GR}(p^2,m)}w^{Tr(ax)} \right\}$ and $\left\{\sum_{x \in Z^m_{p^2}}w^{b \cdot x} \right\}$ equal?

Let $GR(p^2,m)$ be the Galois ring with $p^{2m}$ elements and characteristic $p^2$. Let $Z^m_{p^2}$ be the cross product of $m$ copies of $Z_{p^2}$ which is the set of integers from zero up to ...
2
votes
0answers
72 views

Probability of a characteristic in Blowfish

I'm trying to understand a cryptanalysis of the Blowfish cipher, and I need to calculate the probability of collision in the cipher's S-boxes. Basically an S-box is a list of 256 semi-random 32-bit ...
2
votes
0answers
69 views

(Please check working) Given RSA encoding function $E: x\to x^{11} \pmod{3737}$ find the decoding function $D$

Please check the working and final answer to the question: Question: Given RSA encoding function $E: x\to x^{11} \pmod{3737}$ find the decoding function $D$ My working: $\phi(3737) = \phi(37) \times ...
2
votes
0answers
81 views

Interesting Characteristic About the RSA Cryptosystem

I know that decryption in the RSA cryptosystem works because$$D\left(C\right)\equiv C^d\equiv \left(P^e\right)^d\equiv P^{ed}\equiv P^{k\phi\left(n\right)+1}\equiv ...
2
votes
0answers
103 views

Feasibility of a cryptography transformation

This is a follow-up of the question: Transformation We are given $$g^{1/(x+m)},$$ (it is not possible to find $\frac{1}{x+m}$ due to the Discrete log problem), can we find a $k$ such that ...
1
vote
0answers
44 views

Finding a point on an elliptic curve

I have an elliptic curve with the equation $ y^2 = x^3 + ax + b $ in modulo p, where p is prime. I also have a point G on that curve. How can I find another point that isn't a multiple of G? I ...
1
vote
0answers
33 views

The number of Balanced Boolean functions

Suppose we have n-variable Boolean function (BF) and we know that the weight of a Balanced BF is $2^{n-1}$. The total number of BFs are $2^{2^n}$, Affine BFs are $2^{n+1}$ and Linear BFs are $2^n$. In ...
1
vote
0answers
38 views

Find f(x,y) = 1 if(x=y) else 0 (f must only do addition/substraction multiplication or division)

This maybe more of a computer science problem but maybe the solution lies in number theory. Given integers x,y, find F(x,y) = 1 if x=y else F(x,y) = 0 The obvious solution Negate( x-y ) cannot be ...
1
vote
0answers
23 views

What is the algebraic normal form of $F(x,y,z)= Trace (\alpha x^{24}) + x^{312} + yz$?

Let $w$ be a primitive element of $\mathbb F_{5^4}$. Let $\alpha=w^{13}$. Define, $F:\mathbb F_{5^4}\times \mathbb F_{5}\times \mathbb F_{5} \Rightarrow \mathbb F_{5} $ as, $$F(x,y,z)= Tr (\alpha ...
1
vote
0answers
79 views

Solving the discrete logarithm using index calculus, finite fields and factor bases.

(a) Let $p$ be the prime 1073741827, with $\Bbb{F}_p$ the corresponding finite field. A primitive root in $\Bbb{F}_p$ is equal to $g=2$. Use a factor base of primes up to 13 to find the discrete ...
1
vote
0answers
29 views

statistical analysis of discrete (non-uniform) p-values: cryptographical random data test

i'm doing a statistical analysis of a well-known cryptographic algorithm and have hit an anomaly. i need to prove that what i have found is statistically significant. i am taking block sizes of 256 ...
1
vote
0answers
26 views

Single-Digit Errors

I've been assigned the following homework problem: Given an eight digit number $a_1a_2...a_8$ and a check digit $a_9$, $7a_1+3a_2+9a_3+7a_4+3a_5+9a_6+7a_7+3a_8+9a_9 \equiv 0 \mod{10}$ ...
1
vote
0answers
47 views

determining the next random number pseudorandom number generator?

I have given 3 numbers let's say basic example x_0=5, x_1=6 and x_2=2 and modulus p is 7, ...
1
vote
0answers
83 views

Rank of Quadratic Form

Let $n,m, s \in \mathbb{Z}$ be integers satisying $n=s^2$ and $m=2n$. Let $\newcommand{\bigmatrix}[1]{ \begin{pmatrix} #1_1 & #1_2 & \cdots & #1_s \\ #1_{s+1} & #1_{s+2} & \cdots ...
1
vote
0answers
42 views

Closest vector problem

Given is a vector $v=\begin{pmatrix}2,&-1,&0,&1\end{pmatrix}$ as the shortest vector of the lattice $\Lambda (B)$, where $B$ is determined as $B=\begin{pmatrix}4 &-3 & 2 & 0\\ ...
1
vote
0answers
70 views

Help with Identifying Cipher

Anyone know what type of cipher this might be? 222132143135533 3335521 2214124313 135 35135 353314142412 31253435 313135 1434 2225313554 135 2425333513 351314333545341444 351314333545341444 ...
1
vote
0answers
61 views

Given odd number $n$ count the bases to which $n$ is Euler pseudoprime

As the title says we are given an odd number $n$ and wish to find the number of bases $b$ such that $n$ is an Euler pseudoprime; That is, $\gcd(b,n)=1$ and $b^{(n-1)/2} \equiv \left( \frac{b}{n} ...
1
vote
0answers
94 views

Mathematical foundation crisis and the RSA

I am currently in my last year of high school and I am writing a report on cryptography from a idea historical and mathematical perspective. I am including a few of the subjects: Cantor's diagonal ...
1
vote
0answers
84 views

Understanding Quadratic Sieve Algorithm

I am studying Cryptography and came upon the quadratic sieve algorithm. However, I am having hard time understanding how the algorithm works. I kind of understood how the steps are followed through ...
1
vote
0answers
45 views

If P = NP can asymmetric key exchanges still exist?

One functions are easy to compute (ie polynomial time checking) but hard to reverse. if P = NP does that mean that asymmetric key exchanges will be reduced from polynomial computation time and ...
1
vote
0answers
65 views

Decrypting a message without the Private Key

I am given 5 different encryption modulus, N, each ranging from 78 to 88 numbers long. Then for the encryption exponent, each has the same which is 5. Then I am given 5 different encrypted messages, ...
1
vote
0answers
63 views

Asymmetric block ciphers?

Any block cipher transforms a block of $N$ bits into another block of $N$ bits based on a $\mathcal{K}$ bit key. This can be considered to be a substitution cipher on an alphabet consisting of $2^N$ ...
1
vote
0answers
76 views

Decryption of an Encrypted Message

Suppose we are given sending a message to two people: A and C. A and C have the same RSA encryption modulas: R=(some arbitrary number, say) 454564515456465465465156. But A and C have two different ...
1
vote
0answers
45 views

Why the following observations regarding lattices hold?

The following is an excerpt of a recent paper on lattice cryptography: Let $n$ and $q$ be integers [...], and let $\beta > 0$ . Given a uniformly random matrix $A \in \mathbb Z^{n \times m}_q$ ...
1
vote
0answers
40 views

Discrete Logarithm Problem in $\mathbb{F}_{p}$ and using Elliptic curves

I want to learn about the hardness of the DLP in $\mathbb{F}_{p}$ and using Elliptic curves, and the best attacks against each. I want to be able to compare the hardness of the problem in the two ...
1
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0answers
50 views

Questions regarding the use of Index Calculus for finite fields and elliptic curves

Ok I have a few questions that hopefully some people can answer: For the Index Calculus applied to the Discrete Log Problem in $\mathbb{Z}_p^*$. I first thought that if we could find the ...
1
vote
0answers
65 views

Is discrete ultralogarithm harder than discrete logarithm?

Is computing $g^{xy} \bmod{s}$ from $g^{x} \bmod{s}$ and $g^{y} \bmod{s}$ easier harder or the same level of difficulty as computing $g\uparrow\uparrow(xy) \bmod s$ from from $g\uparrow\uparrow x$ ...
1
vote
0answers
44 views

Adding and multiplication in jacobian coordinates

Please tell me how i can to derive formulas for adding and multiplication of 2 points in jacobian coordinates $((x,y)=(\frac{X}{Z^2},\frac{Y}{Z^3}))$ over elliptic curve? Thanks a lot beforehand. I'm ...
1
vote
0answers
51 views

Efficient decoding of irreducible binary Goppa codes and the role of matrix P in McEliece cryptosystem

If we assume that the support for an irreducible binary Goppa code $\gamma_1, ..., \gamma_n$ is publicly known, when is it possible to efficiently decode the code? I know it's possible if one knows ...
1
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0answers
81 views

Mathematical Basis of OAuth Encryption

There are numerous explanations of the common public-private key system available online, explaining how large primes are used to encrypt messages. Is there any similar guide to the mathematics of ...
1
vote
0answers
282 views

Diffie-Hellman key exchange public key calculation

I encountered a question that I can't seem to get around it. Lets say user A and B uses the DHKE defined over $GF(2^8)$ induced by the irreducible polynomial $x^8 + x^4 + x^3 + x^2 + 1$ and the ...
1
vote
0answers
132 views

How to proof this equation without calculating the values it self

I have the following equation. $$(X + a)^n\equiv(X^n + a)(X^r - 1)\bmod n.$$ This is part of the AKS algorithm. The problem is, that I'll have to solve this equation for every $1\leq a<10$ and ...
1
vote
0answers
50 views

Algorithms for Performing Large Integer Matrix Operations w/ Numerical Stability

I'm looking for a library that performs matrix operations on large sparse matrices w/o sacrificing numerical stability. Matrices will be 1000+ by 1000+ and values of the matrix will be between 0 and ...
1
vote
0answers
412 views

Cryptography puzzle

I'm currently broadening my knowledge in cryptography (or, at least, am trying to) and so I stumbled upon a puzzle I can't crack. It goes like this: You're given a set of pairs. The second number is ...
1
vote
0answers
85 views

A variant of the “closest vector problem” (CVP) in lattice-based cryptography

Consider a public-key scheme on lattices, such as GGH. The private key is a basis $\mathbf{B} \in \mathbb{Z}^{m \times n}$ of a lattice $\mathcal{L}$ with good properties (such as short nearly ...
1
vote
0answers
68 views

Finding the random $r$ in a Paillier encrypted message with knowledge of the private key.

In the Paillier cryptosystem, suppose that I know a Ciphertext encrypted with some unknown random $r$ i.e. $$C = (g^m r^n) \bmod n^2 $$ I know $g, n$, the prime factorization of $n$, i.e., $pq$. I ...