Questions tagged [cryptography]

Questions about the construction and analysis of protocols and algorithms for secure computation and communication (including authentication, integrity, and privacy aspects).

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54 views

Why is M^e mod N the ciphertext and not just M^e

I watched a video on why the RSA algorithm works and it said that $(M^e \bmod N)^d \mod N = M^{ed} \bmod N$ which makes sense if $M^e$ is smaller than $N$. Would $M^e$ not be smaller than $N$, the ...
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2answers
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If someone has an encrypted message and it's original plaintext, could he guess the private key if it's the one used to encrypt the message?

In digital signatures, the private key is used to encrypt a (hashed) message and the public key is used to decrypt it. This made me wonder since the receiver has the cipher text (digital signature) ...
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2answers
24 views

Product of polynomial with negligible function is negligible

I want to prove that for every positive polynomial $p(n)$ and any negligible function $negl(n)$ the product $negl(n)p(n)$ is also negligible. This is what I tried so far: $\forall n>n_0:negl(n)<...
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1answer
35 views

Examples of cryptographic methods using outside randomness

Most cryptographic protocols like pseudorandom number generators run only on "internal" information: that is you set a seed and the next state is a function of its previous state etc.. I am ...
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1answer
103 views

Is it possible to write a program that is able to recognize some source-code as being its own source code?

Is it possible to write a program that is able to recognize some source code as being its own source-code? Biological organisms evolved the ability of kin-recognition, and later, self-recognition, ...
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1answer
170 views

Is the differential privacy definition with lower and upper bound equivalent to the definition with just an upper bound?

According to Wikipedia, given a randomized algorithm $\mathcal{A}$, two neighboring datasets $D_1, D_2$, a real number $\epsilon > 0$, $\mathcal{A}$ provides $\epsilon$-differential privacy, if $$ \...
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1answer
22 views

Not CPA secure for CBC mode if some code are changed that is if we replaced a function $\pi(k,x)=k\oplus x$

Consider the CBC mode where the block cipher is replaced by a function $\pi$ where $\pi(k,x)=k\oplus x$. Show that the mode is not CPA secure. I am not got how to proceed to solve this question. ...
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90 views

What algorithm is prefered to do a x b mod P with big numbers (256 bits)

I'm trying to implement multiple precision arithmetic operations modulo P, with P < 2^256. More specifically, ...
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1answer
902 views

How are extremely large integers stored and implemented in programming languages?

We have data types like int and long etc. which can store just a few bytes of integers. But when we are implementing ...
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1answer
31 views

Factor $n$ in RSA if we know $φ(n)$

If we know that $n = 1363$ and $φ(n) = 1288$, how can we factor $n$?
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1answer
20 views

Is it possible to have a zero knowledge proof with a P Prover?

In the literature, when reading about zero knowledge proofs, the prover (prover/verifier) is always given an unlimited computational power or just capacity to solve NP. Is it necessary for the prover ...
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1answer
27 views

Zero knowledge proof - case of graph 3-coloring (not understanding the concept)

In zero knowledge, in the context of graph 3-coloring, I do not understand how the prover is actually showing that he solved the problem. The context: both know the graph (the prover and the verifier)...
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How to prove that existence of one-way functions implies P≠NP?

Wikipedia: The existence of such one-way functions... would prove that the complexity classes P and NP are not equal. How is this proved?
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Why do public key systems involve private keys?

I read up the definition of a public key cryptosystem. It mentions there is a public key and a private key. That's confusing. Why is it called a "public key" system if it involves a private ...
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1answer
178 views

What are the advantages of using PRNG over TRNG?

True random number generators use an unpredictable physical means to generate numbers, whereas pseudo-random numbers utilize mathematical formulas to produce a certain sequence of numbers that will ...
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1answer
52 views

How 'Avalanche Effect' got its name?

I wonder how or why Avalanche Effect got its name. Avalanche Effect is a desirable property of cryptographic algorithms, wherein if an input is changed slightly (...
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1answer
38 views

NSA Recommended Cryptography Algorithms changes from a single paper

I know that the NSA has recommended cryptography algorithms, such as their A/B suite algorithms and their Commercial National Security Algorithms Suite. I also know that they change their ...
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1answer
86 views

Hardcore bit of a one way function

Let $b:\{0,1\}^*\mapsto \{0,1\}$, be a hardcore bit of a one way function $f$. I want to show that $\vert Pr_{x\in U_n}[b(x)=1]-Pr_{x\in U_n}[b(x)=0]\vert=n^{-\omega(1)}$. Intuitively, it looks ...
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1answer
47 views

Show that if the discrete log problem is $(T,1-\epsilon)$-hard, then it's $(O(\frac{T}{\frac{1}{\epsilon}log\frac{1}{\epsilon}}-nlogm),\epsilon)$-hard

Show that if the discrete log problem is $(T,1-\epsilon)$-hard, then it's $(O(\frac{T}{\frac{1}{\epsilon}log\frac{1}{\epsilon}}-nlogm),\epsilon)$-hard Let $G$ be a cyclic group of size $m$, and let $g ...
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1answer
33 views

Strengthening a given attack on discrete log

I am trying to prove the following claim: Let $(G,*)$ be a cyclic group of size $m$ with generator $g$. Assume there exists some adversary $A'$ of size $T'=\frac{\left(T-O\left(\log m\right)\right)}{...
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1answer
114 views

Time estimation for successful brute force attack

If I have a password = "passwordPASSWORD" and the time it takes to encrypt the password successfully is: 353259.545 nano seconds is there a formula that can work out the time taken to ...
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1answer
36 views

Check if a linear function or an affine function can be a pseudo random function

Let $G = \{0, \cdots , p-1 \}$ be a field. Let $K = G^{m \times n}$ and $F:K \times G^n \to G^m$ be a family of functions. For $A \in G^{m \times n}$ and $x \in G^n$ we have $F(A,x) = Ax$. I need to ...
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1answer
36 views

If there is an algorithm $A$ that guesses the entire message, given an encryption, with probability of $0.2$, then it's not $(O(A) +O(n), 0.1)$-secure

Let $(E,D)$ be a cipher with message space $M = \{0,1\}^n$ and key space $K = \{0,1\}^n$. Assume that there is an algorithm $A\colon \{0,1\}^n \to \{0,1\}^n$ of size $T$ that given an encryption of a ...
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1answer
83 views

Connection between Pseudo random generators and hardness

For a boolean function $f:\{0,1\}^n\longrightarrow\{0,1\}$ $H_{avg}(f)$ is defined as the largest $S(n)$ s.t. for all circuit $C_n$ of size $S(n)$, $\Pr_{x\in U_n}[C_n(x)=f(x)]<1/2+1/S(n)$. Here $...
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1answer
54 views

Cryptosystems whose hardness depends on solving the halting problem?

There has been a lot of work on building cryptosystems whose general security guarantees are attached to famous complexity classes. This post Gives a list of some famous cryptosystems whose underlying ...
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Permutation with stable partitions

I am searching a fast pseudo-random permutation function with the following requirements. Given a predefined set of values $V$ and an integer $k$. Split $V$ to $k$ subset, and iterate over any subset ...
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0answers
48 views

Non-Interactive Zero Knowledge Proofs: zk-snarks and zk-stark

I read up on an abstract example of ZKPs (the cave and the door), but I'm trying to understand NIZKs (specifically zk-snarks and zk-stark). All the examples I can find online seem to have some ...
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1answer
76 views

Is there any neutral element for the cryptographic hash function SHA256? (or its variants)

My question is Is is possible to compute a string given that after applying a SHA256 function the result is the same string?
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71 views

Books for learning Cryptocurrency

Please suggest a good for mathematical section of studying cryptocurrency.
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1answer
90 views

Manually Performing ECB & CBC

I am learning about block ciphers and while I understand the concept of Electronic Codeblock mode and cipher block chaining, I could not find any relevant practical examples online. Can someone ...
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114 views

Undetectable error correcting codes

I have a 256 bit string (indistinguishable from random) which I wish to encode into a greater length string using an error correction code. The result must also be indistinguishable from random. It ...
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Asking for your help with LFSR, linear automaton

I am a software developer new to the site. I am currently learning about LFSR (linear feedback shift register). Every day I solve a question which is given to me, but today I am lost. I can not solve ...
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1answer
43 views

One-way function is not injective when it is in NP

Let us $\Sigma = \{0,1\}$ and $f: \Sigma^* \rightarrow \Sigma^* \in FP$ for which is valid that $\exists k: \forall x \in \Sigma^* : \lvert x \rvert ^ {1/k} \leq \lvert f(x) \rvert \leq \lvert x \...
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Accessible CS Math Job [closed]

I am a CS undergrad and a huge enthusiast of pure math. I have been doing competitive programming and proofs for a while. My ambition is to become an academic in theoretical computer science. The ...
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2answers
109 views

Decryption of RSA

How can we decrypt an RSA message if we only have the public key? For example, Message: 21556870,12228498 Public Key: ...
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1answer
89 views

How to perform matrix multiplication in Mixing Columns step of AES?

I am studying AES and trying to implement it. But I am having difficulty understanding the Mixing Column step. In that step we have to perform matrix multiplication between the state matrix and ...
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0answers
19 views

Converting Smart Contracts into Arithmetic Circuits [closed]

Are there any existing programs available to convert smart contracts into Arithmetic Circuits with which I can implement and experiment with Secure Multiparty Computation (MPC) protocols?
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Absolute limit in Huffman encoding

I have computed the average code length using the Huffman encoding. Now, I am asked to compare the average code length with Absolute limit but I ain't sure about the absolute limit here is :( Could ...
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0answers
22 views

Extracting text from a hidden image

Say i have cropped an image and have hidden some part of it, like shown below Is it possible for anyone to download this image and able to decipher what the hidden text is?
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24 views

Abusing ElGamal in order to attack a known encrypted text

I saw a very interesting question regarding Elgamal cryptosystem that I don't know its answer. It is really interesting and I would be very happy if you could elaborate on it and explain the tricky ...
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0answers
26 views

equivalent sub-keys in DES encryption

i am trying to understand the DES cryptosystem and was wondering: what would've happened if all of the sub-keys were equal? does it reduce the security? can we actually find the keys if we know all ...
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1answer
116 views

Period of sum of two periodic sequences

I was wondering, what is to be the shortest possible key using Vigenere encryption, if a text is ciphered one time with a key of length $i$ using Vigenere and second time with a key of length $j$ ...
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1answer
128 views

Determining key from plaintext and ciphertext (Vigenère)

I was wondering why mathematically we can know the key in the Vigenère cipher if we know in advance a message and its encryption.
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Is 'the bombe' technically a computer?what is technically meant to be a computer?

Some say that 'the bombe' created by Alan Turing is technically not a computer despite decrypting the codes. Why is it so? Is 'the bombe' technically a computer? First of all what is technically ...
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1answer
32 views

Solve SUBSET SUM for Reciprocals of Primes

Let $p_1, ..., p_n$ distinct prime numbers with $P = \prod_{i=1}^{n}{p_i}$ and $A=(a_1, ..., a_n)$ with $a_i = P/p_i$. Problem Show the SUBSET SUM problem $(A, \alpha)$ can be solved in polynomial (...
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533 views

If current time in milliseconds is considered good enough random seed for a pseudorandom number generator, why not just use that time directly?

I was reading about pseudorandom number generators and how they need a seed and how that seed is usually current system time in milliseconds. One of the most common algorithms is the linear ...
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1answer
34 views

Cryptography: Play Fair cipher

In our university, we were taught that since all 26 letters cant be placed together in a $5*5$ square matrix we must put $i/j$ together like this represented in the below diagram. Here our key is $...
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1answer
65 views

Diffie-Hellman and its disadvantage with large primes

I was reading our university slide on the Diffie-Hellman where it is mentioned that one of the disadvantages of D-H is that For large prime, $p-1$ is an even number so, $\mathbb{Z}^*_p$ will have a ...
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2answers
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What are the elements of the modular ring mod 7? [closed]

Are the elements of a modular ring simply the set of all the numbers from 1 to p−1? in this case p−1 = 6 ? I asked this on the math stack exchange https://math.stackexchange.com/q/3375667 and was ...
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1answer
49 views

Weaknesses arising from using same key in both channel directions

I came across the following question: Which of the following risk may arise, when same key is used to encrypt both directions of a communication channel, that are not present if using different keys ...

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