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

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question about cryptography

Sam and Tim have set up their RSA keys (eS; n); (eT; n), respectively, where the n-value is the same. Furthermore, it happens that gcd(eS;eT) = 1. Suppose that their friend Rob wants to send both Sam ...
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1answer
28 views

Validity of ElGamal signature variation

I'm trying to solve excersise 7.6 from Hoffstein - Introduction to Mathematical Cryptography page 459 (hhttp://goo.gl/oRyInT) Let $p$ be a prime and let $i$ and $j$ be integers with $gcd(j, p − 1) = ...
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121 views

Suggest solutions book

Does somebody know solutions manual for book "An Introduction to Mathematical Cryptography" by Jeffrey Hoffstein, Jill Pipher, Joseph H. Silverman?
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248 views

How to deal with negative exponents in modular arithmetic?

So I think I understand how to calculate something like $(208\cdot 2^{-1})\mod 421$ using extended euclidean algorithm. But how would you calculate something like $(208\cdot2^{-21})\mod 421$? ...
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64 views

graduate level introduction to elliptic curve cryptography

I am looking for a good modern book / lecture-notes about elliptic curve cryptography. Does anyone have good recommendations?
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1answer
43 views

A Very Elementary Article or Webpage about Secret Sharing

I'm looking for an article or webpage about secret sharing with Latin squares, accessible to middle school students. I searched but found none. Can you help me? Thanks.
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31 views

Trouble Understanding Pinocchio (Verifiable Computing) Sparse Polynomials

I hope I'm asking the question properly. I've never asked anything on this exchange before, but I didn't know where else to ask. The paper in question I've almost got all the pieces to understand can ...
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1answer
31 views

Multiply point by scalar in elliptic curve group

I'm trying to understand how to multiply a point by a scalar to get a point in elliptic curve cryptography. Here's an example from my textbook. The group is E257(0, -4). That's shorthand for y2 = x3 ...
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1answer
49 views

Code that can be generated from 3 of 5 trusted people?

Suppose a computer contains sensitive data protected by a 3-digit passcode. (I understand this does not provide much security in the real world, but for the sake of the problem, assume only 3 digits.) ...
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39 views

Drawing a 5-stage binary LFSR with feedback Sm+5= Sm + Sm+1

Any guidance on how to draw this would be greatly appreciated I know this is more of a visual thing but I also want to go on to determine all the possible (different) cycles that are generated by this ...
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1answer
53 views

Proof related to RSA decryption

Can someone help me with this proof: Show that RSA decryption works for all messages a as long as the modulus m is a product of distinct primes. Thank you.
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1answer
45 views

Are chaotic function one way?

Are chaotic functions also one way functions? Can they be used in cryptography?
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1answer
45 views

Multiplication in the Galois field GF(3^3)

I am trying to compute $x^3$ in the Galois field $\text{GF}(3^3)$ using the irreducible polynomial $f(x) = x^3 + 2x^2 + 1$. From the expression $x^3 = f(x) + (2x^2 +1)$ I proceed to take the modulus ...
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31 views

Calculation of polynomial in the finite field

I'm trying to understand the McEliece cryptosystem and I'm looking to this paper http://www.mif.vu.lt/~skersys/vsd/crypto_on_codes/goppamceliece.pdf On page 26 they are calculating syndrome and ...
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1answer
37 views

RSA cipher Encryption with $n=210757$ and $a=3$ and Decryption with $n=14659$ and $a=3$

I think I understand correctly how to encrypt something with an RSA cipher, but I am a little lost on how to find the decryption key...(also I apologize for the formatting errors) An RSA cipher is ...
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1answer
25 views

Find $D$ in RSA cryptosystem

For the following encryption key $(n, E)$ in the RSA cryptosystem, compute $D$. $(n, E)= (451, 231)$ So I know $n=11*41$, so $m=400$. Now $D=$ inverse of $231 \ (mod \ 400)$. However I am not sure ...
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1answer
81 views

attack on RSA (factoring when knowing e and d)

This is the problem, I have to explain how works the algorithm on the image with modular arithmetic for a discrete math class., I tried to explain it, but I couldn´t. In the class, I have seen this ...
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0answers
15 views

Shamir sharing scheme - Calculating shares

In a (2, 5) Shamir secret sharing scheme with modulus 23, two of the shares are (1,22) and (4,8). Find the secret. $$S(1) = M + s = 22 (mod 23)$$ $$S(4) = M + 4s = 8 (mod 23)$$ Eliminate through ...
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1answer
50 views

finding the inverse of a matrx

In order to decrypt a cipher text using hill cipher, we must first find the inverse matrix of a given matrix. From this link http://en.wikipedia.org/wiki/Hill_cipher, ...
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1answer
39 views

Derivative of Diffie Hellman

Looking to get some clarification on this. We have the same three protagonists, Bob and Alice, trying to send each other a message. And Eve trying to figure out the message sent by Bob and Alice. ...
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1answer
35 views

Something similar to Euler's theorem

If $p$, $q$ are not equal primes. $n=pq$, $\varphi(n) = (p − 1)(q − 1)$, $d = \gcd(p − 1, q − 1)$. Is it true that for any $a$ such that $\gcd(a, n) = 1$ holds $a^{\frac{\varphi(n)}{d}} \equiv 1 ...
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1answer
48 views

Decryption of a RSA encrypted message is not working.

Using RSA with e=13 (encrypting power), d=17 (decrypting power) & n=33 (RSA modulus) I noticed that once I decrypted the encrypted message it would be different then the original message. Why is ...
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1answer
78 views

Toy cryptographic hash function for education purposes?

I'm teaching some high school students about number theory and cryptography, and I'd like a hash function (or ideally, a family of hash functions) that I can use as simple demonstration for ...
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1answer
149 views

RSA Algorithm Question [duplicate]

Suppose the primes p and q used in the RSA algorithm are consecutive primes (meaning they differ by 2). How would you factor n = pq? The ciphertext 10787770728 was encrypted using n = 10993522499 and ...
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1answer
70 views

Is there an error-correcting code where almost every word could be used as a codeword?

An error-correcting code for strings of length $n$ from a $K$ letter alphabet is a partition $\Pi$ of $K^n$ together with a choice function $\pi$ on $\Pi$. Let $A_i$ for $i<M$ enumerate $\Pi$, and ...
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1answer
34 views

Number of bits needed for Huffman code

Jake uses a Huffman code to compress i.i.d. (independent nad identically distributed) strings of symbols that come from a 5-ary alphabet ($A$, $B$, $E$, $R$, $S$) where the probabilities of occurrence ...
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2answers
334 views

Distribution of the RSA numbers

Let's take a random prime $p$. For the sake of the argument let's say $\log(p)\approx 1000$. Let's suppose all numbers between $p$ and $p+1000^2$ are composites. What is the approximate probability ...
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24 views

Two-dimensional affine cipher

Problem: We have a two-dimensional affine cipher with $n = 2,\,\,\,\mathcal{P} = \mathcal{C} = {\mathbb{F}_{16}^2}$, where $\mathcal{K} = \{ A,\,\,b\} $ and $b = (0,0)$. The encryption and decryption ...
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1answer
88 views

Decrypting a Vigenere cipher with affine key

Consider a cipher where the method of encryption is to perform a Vigenere cipher on a plaintext, with the key word being an affine cipher of the letters a,b,c,...,z. How strong would this cipher be? ...
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2answers
24 views

reducing exponent in modular arithmetic

Im struggling with an example excercise because I have problemes to comprehend an step in the calculation $3^{36} \mod 59 = 3^{7} \mod 59$ How can I reduce the exponent $36$ to $7$? I tried it with ...
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1answer
72 views

Does Zhang's result on primes makes RSA weaker?

I read from Finnish newspaper ( http://www.uusisuomi.fi/tiede-ja-ymparisto/72212-matemaattinen-ongelma-eli-2-300-vuotta-mies-subway-tiskin-takaa-ratkaisi#.VBwhYp09F2k.facebook ) the article of Zhang's ...
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0answers
75 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 ...
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37 views

Cryptography probability

62% of plaintext messages have even parity. 56% of odd plaintext messages have ciphertext with even parity. 48% of even plaintext messages have ciphertext with even parity. What is the probability ...
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1answer
39 views

The modular n-th root (mod p*q)

I am interested in the solution of the following modular equation. Is the solution unique? If not, how difficult do find more than one solutions? $$x^n \equiv a \; \bmod (p\cdot q)$$ where $p$ and ...
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1answer
30 views

Affine cipher and shift cipher

I have the following question: An affine cipher with key $K(0,b)$ is equivalent to a shift cipher explain why I don't think this is true, and assume it is a typo, $K(1,b)$ I would agree, since ...
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41 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 ...
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1answer
27 views

Cayley table for 2-bit integers ${Z_4}$

Let us consider the multiplication operation, denoted by $ \odot $ on the set of 2-bit integers ${Z_4}$ defined as follows: $$\eqalign{ & a \odot b = (ab\,\bmod \,5)\,\bmod \,4\,if\,a \ne 0,\,b ...
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1answer
32 views

Matrix in polynomial field

We are given a matrix $$M=\begin{pmatrix}0&1&1\\1&1&0\\1&1&1\end{pmatrix}$$ I need to show that $M$ represents multiplication by element $\beta $ in the field $F = ...
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1answer
24 views

$A^{-1}x \pmod{26}$ and coprime requirement in Hill cipher

I am reading Hill cipher from wiki page and I have been stuck on this thought for a while. Why is there a requirement for $\det(A)$ and $26$ to be coprime in Hill cipher ? Anybody familiar with Hill ...
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1answer
41 views

Notation symbol $x$ for functions

On the Modern Stream Ciphers slide #6, the following expression is used: $$ \{0,1\}^s × R ⟶ \{0,1\}^n$$ What does $×$ mean? I've seen $×$ used in a few other contexts, and I suspect it means ...
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2answers
111 views

Why does this method for the average salary problem fail?

In my Computer Science class, we were introduced to the Average Salary problem, where a group of people want to determine their average salary, but they don't want anyone to be able to determine the ...
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25 views

Cryptography: Hill Ciphers

Recently, I was given three ciphers to crack for my cryptography class. At this point, I have guessed that one of them is likely a Hill cipher (probably 3x3, as that is the most complex we have done ...
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1answer
306 views

How to determine the key-matrix of a Hill cipher where the encrypted-message-matrix is not invertible?

I am new to this subject and I have a homework problem based on Hill cipher, where encryption is done on di-graphs (a pair of alphabets and not on individuals). The alphabet domain is $\{A\dots ...
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1answer
22 views

Exponention cipher - prove unique mapping from plain text to cipher text

At the heart of RSA, is the exponention cipher: C=M^e mod P (where C=ciphertext, M=Plaintext e=exponent and P=modulus.) How do you prove that two different plaintexts don't map to same ciphertext?
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2answers
96 views

Irreversible Math Function

Is there any function which will take two inputs, (a+b) as one input and c as another, and return a result from which c can only be computed only if a and/or b are known individually? Basically I ...
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51 views

Is it possible to find plaintext from ciphertext if (n) and (a) are known?

I have a couple of questions pertaining to a RSA problem. I need to decipher some ciphertext and find out what the original plaintext was. n = 2537 and a (or the exponent) = 11. Encrypting function: ...
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3answers
49 views

Is 6 a generator of this Group?

I've had the opportunity to learn about the mathematics behind Diffie-Hellman key exchanges, prime numbers, generators of groups, and all that good stuff. I wish I understood it, it's discomforting ...
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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 ...
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2answers
55 views

Find the $4$ sq. roots of $100$ in $ U_{209}$. Identify which square root of $100$ is square.

Find the $4$ sq. roots of $100$ in $U_{209}$. Identify which square root of $100$ is square. (Not the $4^{th}$ root, but the $4$ square roots). I honestly don't even know what this question is ...
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1answer
131 views

If the same message is sent to Alice and Bob who are using different public keys, how can somoene following the channel find $m$

Alice and Bob are using different public keys, Alice is using ($N_{1,2}$) and Bob ($N_{2,2}$). A message, $m$ is sent to both of them using their RSA systems. It is also true that $N_1$ and $N_2$ are ...