# All Questions

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### What RC4 key value will completely invert $S$ after initial permutation?

What RC4 key value will completely invert $S$ after the initial permutation, so that $S[0] = 255, S[1] = 254, …, S[254] = 1, S[255] = 0$?
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### Given p and q of DSA how do you show they are prime?

I am given p = 4916335901 q = 88903 and am asked to show these are prime as well as q|(p-1) in DSA. I am unsure on how to ...
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### Is $H(x) = x^2 \bmod p$ pre-image resistant, second pre-image resistant and/or collision resistant

I have the function $H(x) = x^2\bmod p$ , where $p$ is a prime of length n bits and this function maps to the message $x$ to a n-bit hash value $H(x)$. I need to find out if it is pre-image ...
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### Can a monoalphabetic substitution cipher attain perfect secrecy?

Can a monoalphabetic substitution cipher attain perfect secrecy? Definition of perfect secrecy: $${\rm Pr}[\,{\rm Enc}_k(m_1) = c\,] = {\rm Pr}[\,{\rm Enc}_k(m_2) = c\,]$$
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### Question on RSA trapdoor permutation

You plan to use a public-key cryptosystem based on the RSA trapdoor permutation in three different real-life applications, in which the attacker has, respectively, only one of the following resources: ...
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### Problem implementing MixBytes functionality in Groestl

Disclaimer: School work. I am trying to implement Groestl through Java, and have got stuck on the MixBytes section which can be found here section 3.4.5 page 11. As per the description of matrix ...
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### how to use salt to sign a message and how is it effective? [duplicate]

I've had an assignment to sign a file using hash and salt, so I read about salt and I got why it's important when it comes to password, but not to sign messages. How do I sign something using salt? ...
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### Looking for a detailed example of proof by reduction

I'm looking for a very detailed example of proof by reduction. Say we have two or three protocols (that have been proven secure) and we construct a new protocol. We want to provide a proof of security ...
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### derangements and permutations in cryptography

Given a partial key for a mono-alphabetic substitution cipher (missing 11 letters), calculate the number $N$ of possible keys, given that no plaintext letter can be mapped to itself. ...
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### Encryption of numeric value using playfair

I am studying in CSE and in my recent exam paper, A question was asked as: Construct a playfair cipher for Plaintext: semester5 and key:technology. Generally as we are taught yet, there is no ...
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### m ∈ Zn \Z*n, RSA works but not secure

If you happen happen to have a message m ∈ Zn \ Z*n, RSA works but not secure. How likely is it going to happen? |n|=1024 bits |p| = 512 bits |q| = 512 bits.
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### Do we need symmetric cryptosystems?

One question I had to answer in my crypto exam today was: Do we need symmetric cryptosystems? As it stands, that's probably a debatable question, so I'd like to reformulate this as: Are ...
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### How is the curve equation used in ECC?

I have a hard time learning exactly how the elliptic curve equation is used in the ECC. $$y^2 = x^3+ax+b$$ If someone knows and could explain to me in simple steps how this is done or a link to it ...
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### XOR with constant key in CBC mode

I have a hypothetical encryption scheme where somebody uses the one-time pad in CBC mode. That is, the block cipher is $E(k, m) :=k⊕m$, and that block cipher is used in CBC mode. Now, I am assuming ...
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### Definition of a Statistical Test

In Professor Boneh's online Cryptography course at Coursera, I am a little puzzled by his definition of a statistical test where he writes: A(x) = iff |#0(x) - #1(x)| <= 10.√n Now, if – as ...
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### How do I express each element in a field F as a power of a primitive element?

I have a field $\mathbb F_{2^4}$, and it is represented as a residue ring of the polynomials over $\mathbb F_2$ modulo the polynomial $\beta^4 + \beta^3 + \beta^2 + \beta + 1$. I want to express ...
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### El Gamal encryption scheme and symmetric encryption scheme

Consider the El Gamal encryption scheme, a symmetric encryption scheme (KG,E,D), and the following hybrid encryption scheme having an encryption algorithm that, on input a public key (G,q,g,h), where ...
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### Why do some block cipher modes of operation only use encryption while others use both encryption and decryption?

In Chapter 6, Question 6.8, of his book “Cryptography and Network Security Principles and Practices”, William Stalling asks: Why do some block cipher modes of operation only use encryption while ...
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### CBC MAC and DES combined question?

Suppose that we want to develop a MAC scheme which is as secure as Triple-DES CBC-MAC and at the same time as efficient as Single-DES CBC-MAC. We come up with the following idea: Except the last ...
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### Vernam Cipher with Repeating Key [duplicate]

I'm doing a piece of coursework for Uni and the task is to break a Vernam Cipher. So we have a randomly generated key which is as long as the message. It gets used for all the messages sent from that ...
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### Breaking RSA when some bits of one prime are known

RSA primes are 100 bit. You know first 80 bits of one of the primes. In this system, come up with an efficient way to decrypt the cipher-text. This was the question on my quiz. I'm not sure how ...
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### Symmetric-Key Based authentication [closed]

So i've managed to answer all the other cryptography questions, but I have not come across this exam style question before, and need help.
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### weaknesses in ElGamal with public key of small order

Suppose $p=29$, $\alpha = 2 \in F_p^*$ is a generator of $F_p^*$. Bob picks $d \in \{2,...,27\}$ such that $\beta = \alpha ^d=28 \pmod{29}$. He then sends his $(p,\alpha ,\beta)$ to Alice who herself ...
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### Chosen Ciphertext Attack with a theoretical decryption machine

Say we have an encryption algorithm that encrypts data blocks of 128 bits size, and makes them cipher blocks $C = E(P)$ without chaining. Also assume there is a linearity rule for XOR: For every pair ...
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### Integers in ECC

Let A be a point on curve with integral coordinates. Does k.A necessarily have integer coordinates? If so than why and if not than how to find A and k such that k.A has integral coordinates.
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### Number of different substitution alphabet ciphers possible with given conditions?

If you consider a 26 letter alphabet, and a cipher where 24 of the letters are sent to themselves, and only 2 letters switch, how many different substitution alphabet ciphers are there, and what ...
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### Must the ciphertext be longer than the key for symmetric encryption?

I am planning to encrypt the different fields of a database independently, using a symmetric encryption scheme (probably 3DES). Since some of the fields are as small as an integer, may that be ...
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### Multiplication-homomorphic schemes

I'm looking into multiplication-homomorphic schemes now and basically I see that there are 3 options: RSA, Boneh-Goh-Nissim and ElGamal. RSA was proved to be insecure unless message is randomly ...
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### Can I create a fixed length output from a fixed length input?

I use AES256 for various purposes in my app. However, the purpose I am now trying to achieve is the following: Input is for example AU00000001 and I would like a ...
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### Commutative Encryption with RSA scheme?

I wanted to know how I could manage to do what I'm going to tell you next, with the RSA encryption/decryption scheme. So Alice and Bob each have a public key $(n, e)$ and a private key $(p, q, d)$; ...
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### Modulo properties of two prime numbers

I am supposed to prove that x = y mod (p*q) <=> x = y mod p and x = y mod q with p and q are prime numbers. It somewhat sounds reasonable to me, but unfortunately I don't have any clue how to prove ...
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### Three different numbers with x³=x mod p

p is a prime greater than 2 and $a \in \mathbb{Z}_p$. Why are there exactly three solutions for a³ = a mod p? Obviously 0 and 1 are both in $\mathbb{Z}$ and valid solutions, but that still means, ...
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### How (in)secure is a signature based on DSA with DSS1 (SHA1) in reality?

As I found out the OpenSSL implementation provided by PHP (openssl_sign) only allows DSS1 as the hashing algorithm for DSA signatures (see also my related question). I’d prefer DSA over RSA in my ...
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### Pick faster private exponent

I recently tried to send 1536-bit modulus CSR to COMODO. They refused to sign the certificate. I later found out that it's because NIST mandated 2048-bit modulus on the SSL certificate. I think it's ...
118 views

### Is there an oblivious decryption scheme?

Alice has $K$; Bob has $E(K, m)$; Is there such a scheme that enables Alice decrypts $E(K, m)$ without knowing $m$, and Bob gets $m$ ?
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### Twisted curves in protocol

I've come to understand that twisted curves, as for instance defined in the Brainpool specifications, are $F(p)$-isomorphic to their regular $F(p)$ equivalents. So brainpoolP256r1 is isomorphic to ...
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### Encrypt HDD with keyfile and password and allow backing up the keyfile with secret sharing

I want to: Encrypt my whole HDD with a keyfile and a password (meaning that both are required to decrypt it), Be able to back up pieces of the keyfile in several distant locations using Secret ...
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### Question about dual system encryption

Recently, I have been reading some dual system encryption papers. In these systems, is the adversary able to generate “semi-functional ciphertexts”?
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### What is the “artificial abort” technique?

In the security proof of Brent Waters's paper Efficient Identity-Based Encryption Without Random Oracles, he uses a novel “artificial abort” step on page 6. At this point the simulator is still ...
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### Reductionist proofs of decisional problems to computational

Are they any reductionist proofs where an attacker $\mathcal{I}$ for a well established computationally "hard" problem $\mathsf{Π}$ is employing an attacker $\mathcal{A}$ who we assume is able to ...
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### server aid secure equality test

The scenario is like this: $P_1$ has $m_1$, $P_2$ has $m_2$, they want to compare whether $m_1=m_2$ via the server $S$. After the protocol, only $S$ knows the result, and there is no interaction ...
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### Encryption time in ECC

In RSA, encryption time is usually much less than decryption time due to having a small public exponent. Can this be achieved in Elliptic Curve Crypto (ECC)?
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### Use of Different keys with PCBC

Currently I am having a doubt, while making a "DES PCBC" encryption on an image I observe a bit of the silhouette of the image (Probably because of the XOR between plaintext blocks and ciphertext ones ...
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### Proxy re-encryption mod operations

I managed to implement the proxy re-encryption scheme from http://eprint.iacr.org/2009/189.pdf in python 2.7, however I am having performance issues. As it is, I can run the algorithm for key sizes up ...
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### Padding to increase entropy and size of (otherwise) small JSON objects

Maybe this better fits, the security stackexchange... I'm building a web API. We want to enable some relatively simple encryption, instead of going full-blown OAuth2 (which frankly, IMO, sucks). So I ...
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### AES/CBC fixed Initial vector use-case [duplicate]

I am using AES/CBC to encrypt my http cookie. I never encrypt the same cookie value twice so my understanding is I don't need to use a random initial vector - using a fixed initial vector is fine for ...
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### P = NP security implications [duplicate]

If someone finds an efficient way (ridiculous or not) to turn NP into P (such as creating multiple universes, saving the one with the correct answer), would we have any good algorithms for encryption, ...