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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1answer
27 views

will breaking not used anymore RSA codes in the future affect privacy?

just read and watch some stuff on how RSA works. main idea seems to be if someone steals your communication he cannot decode it anyway. but let's say someone steals it and keeps it along with current ...
0
votes
2answers
48 views

XOR of one-way function

Considering the top answer to the question “If xor-ing a one way function with different input, is it still a one way function?”… The function is no longer one-way. we build a counter example ...
1
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1answer
37 views

Is there a zero-knowledge protocol for bit vector agreement?

Suppose Alice knows a secret vector of $N$ bits, say $A=\langle a_1, a_2, \ldots, a_N\rangle$ and Bob similarly knows $B=\langle b_1, b_2, \ldots, b_N\rangle$. Is there a protocol that allows them to ...
0
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0answers
22 views

Are there any classes of functions whose definitions can be easily procedurally generated and have implementations easily procedurally checked, but

Are there any classes of functions whose definitions can be easily procedurally generated and have implementations easily procedurally checked, but for which valid implementations are difficult or ...
7
votes
3answers
284 views

1-to-1 cryptographically secure bit shuffling

Given an input item (N bytes), I'm looking for a function that will map this to an output (still N bytes). The function should have the following qualities: It should be 1-to-1 so that all inputs ...
2
votes
2answers
441 views

What if p and q are not distinct in RSA Crypto System? What could go wrong?

In RSA Crypto System we choose p and q such that they are distinct primes. Calculate n=pq and phi=(p-1)(q-1). Then e is chosen for public key (n,e) s.t. gcd(e,phi)=1
22
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5answers
4k views

Meaning of: “If factoring large integers is hard, then breaking RSA is hard, is unproven”

I was reading CLRS and is said: If factoring large integers is easy, then breaking the RSA cryptosystem is easy. Which makes sense to me because with the knowledge of $p$ and $q$, it is easy ...
0
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1answer
27 views

Issues in RSA setup

Suppose we have public key: $$n= 1015, e= 3$$ and private key: $$d= 635, p= 35, q= 29, \phi(n)= 952$$ For $m = 100$, we have $$c = m^e ~mod~n = 100^3 mod~1015 = 225.$$ To decipher this, let us ...
3
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1answer
35 views

One-shot Private Randomness Extractor

Suppose a pair of random variables $(X,Y)\in\mathcal{X}\times \mathcal{Y}$ with joint distribution $P_{XY}$ is given. I am interested in a deterministic mapping $f:\mathcal{Y}\to \{0, 1\}^k,$ for ...
3
votes
1answer
73 views

Do one way function exist?

I was going through Wiki Page List of unsolved Problems in Computer Science There was a Problem which I do not understand Do one-way functions exist ? [Is public-key cryptography possible ?] ...
5
votes
3answers
57 views

One way recurrence O(N)->O(1)

Imagine we have a random number generator where g(n+1) = f(g(n)), where f is some function (e.g linear recurrence). I'm trying to find a system where it's fast to find many steps in the future ...
7
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2answers
59 views

Running an algorithm on data remotely and ensuring answer has not been tampered with

I´ve been thinking about this particular computing/crypto/database problem for years and I just want to know if there are already solutions to it. To be honest I don´t even know what field this ...
4
votes
3answers
567 views

Encrypting a 180-bit plaintext into a 180 bit ciphertext with a 128-bit block cipher

I have a field in my data store which must take exactly 180 bits of information. Some users will choose to make this data encrypted, some won't, so some of those 180 bit fields will be ciphertext some ...
2
votes
1answer
30 views

If a Ptime function loses x bits of data at every call, is it a one way function?

If we have a computational function $f(x)=g(f(x-1)^2)$, where $g(y)$ is a floating point operation, mapped onto a given number of bits say 32 bits (thus leading to loss of a given number of precision ...
4
votes
1answer
67 views

Hardcore Bit proof for discrete log

I am studying Crypto and am trying to understand why discrete log creates is useful for creating a PRG. More specifically, I want to prove via reduction that $B(x)=(x<p/2)$ is a hardcore bit for ...
4
votes
0answers
26 views

Correctness of a zigzag algorithm to find the most similar vector in a bounded integer lattice

I am currently working on an integer lattice problem, called the "most similar vector problem," and wondering if can be solved correctly by a simple "zig-zagging" algorithm. Given a real vector $u ...
0
votes
2answers
24 views

Show that a function is not a PRFs

I am studying cryptography and having some trouble with the PRFs How do I show that $f_{k}(x) =x+k^2$ mod $2^n$ is not a Psuedo Random function? I know that I need to show that the distignuisher can ...
18
votes
3answers
1k views

Given RSA, why do we not know if public-key cryptography is possible?

I was on wikipedia on list of unsolved computer science problems and found this: Is public-key cryptography possible? I thought RSA encryption was a form of public-key cryptography? Why is this a ...
4
votes
2answers
293 views

Can systems that prevent double-spending (e.g. crypto-currencies) be used to attach other unique data?

The Bitcoin-solution can be described as "[...] a solution to the double-spending problem using a peer-to-peer network. (official Bitcoin paper, PDF, abstract, first page). Now I wonder if a similar ...
3
votes
1answer
35 views

“Most Similar Vector Problem” on an Integer Lattice

I am currently working on problem that I think could be expressed as an integer lattice problem, and hoping to find some guidance on this forum. Given $u \in \mathbb{R}^n$ and a bounded integer ...
2
votes
1answer
32 views

About the definition of “differential privacy” in communication complexity

In the context of communication complexity I see a definition of differential privacy which isn't totally clear to me as to why it makes sense. So the two parties $A$ and $B$ draw two strings $X$ ...
1
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3answers
271 views

Formula for sufficiently lengthy encryption key?

As you add length to an encryption key, at some point the message becomes impossible to brute-force decrypt. This is because at that point, if you go through all the possible keys, you'll get many ...
3
votes
1answer
276 views

If one-way functions exist are we definitely using them?

I know that if one-way functions exist then there are certain universal one-way functions that exist, but to my knowledge they are too impractical to implement (which is the main reason why they are ...
-1
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1answer
39 views

What is the relation between differential-privacy mechanism and entropy?

Why do differential-privacy people care whether or not the noise function saturates the lower bound of Shannon entropy? For example : Laplace distribution that is used to model the noise function ...
3
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0answers
44 views

How is Chinese Remainder Theorem used in the proof of correctness for RSA

Question At the very end of (most) proofs of RSA's correctness we have something like $$m^{ed}\equiv m\pmod p$$ $$m^{ed}\equiv m\pmod q$$ Therefore by the Chinese Remainder Theorem (CRT) ...
6
votes
1answer
135 views

Is there a continuous hash?

Questions: Can there be a (cryptographically secure) hash that preserves the information topology of $\{0,1\}^{*}$? Can we add an efficiently computable closeness predicate which given $h_k(x)$ and ...
0
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0answers
60 views

More about the ESP tree

In this previous question I had asked about the intuition behind looking at the ESP tree. One place where it is used is to construct an approximation of arbitrary distance functions $d : [m]^n ...
4
votes
2answers
216 views

Why is it important to solve a problem in Polynomial time, In cryptography?

I have just started to learn Cryptography. I am trying to learn "Merkle-Hellman Knapsack Cryptosystem". So, right at the beginning of the discussion, a question came in my mind: Why is it important ...
3
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1answer
38 views

What are the examples of the easily computable “wild” permutations?

I am looking for the function $y=f(x)$ that would map the integer interval $[0,n)$ into itself $[0,n)$. The function must be bijective, so it is a permutation of n elements. It should "randomize" the ...
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1answer
67 views

A question on RSA

Why were primes which are $1$ modulo $4$ considered to be weak for use in RSA cryptography (http://en.wikipedia.org/wiki/Blum_integer)? Was there a time it was considered there could be an efficient ...
0
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1answer
78 views

RSA Decryption from Simple Public Key Values

I'm a little stuck trying to figure out how to decrypt some messages and could use some hints as to what I may be doing wrong. I was given a series of integer values that make up my cipher text. Here ...
0
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1answer
67 views

What's the complexity of the Bombe?

Now my knowledge of this comes through watching The Imitation Game, a glance of a wiki article, and a couple of computerphile videos, so forgive me if it's obvious. While watching the Imitation Game, ...
4
votes
1answer
41 views

Computing modular exponent given order

I want to compute $g^{mn}$ mod $n^2$ where $n=pq$ and I know that $g$ has order $kn$ mod $n^2$ where $m<k$. Is there any clever way of doing it utilizing the order? I have tried other methods of ...
1
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1answer
54 views

Hash values that are impossible to reach

I was just curious as to if there are (or could by) any hash values that are impossible to compute due to the implementation of the algorithm. For example, SHA-256 produces a value that is 256-bits ...
1
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2answers
114 views

What is the complexity of finding the two prime numbers a composite number (used in RSA Protocol) is made of?

I am aware that as the number increases in Digits the process of locating the two prime numbers that when multiplied produce the given number is increased as well. I also know that is it somewhat ...
2
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1answer
80 views

Is a very long plain text password harder to crack than a short complicated password? [closed]

Is it true that a password consisting of the alphabet, even of common known names is much harder to find for a computer program than a short password, even though it uses numbers and other characters? ...
0
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1answer
403 views

How to explain the steps in the implementation of hashing functions like SHA1

I was reading the article about the SHA1 hashing function (I know it is not secure anymore) and I've found a pseudocode implementation on Wikipedia. I can see that there are a lot of mathematical ...
10
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2answers
437 views

How does an operating system create entropy for random seeds?

On Linux, the files /dev/random and /dev/urandom files are the blocking and non-blocking (respectively) sources of pseudo-random ...
4
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1answer
64 views

Partially homomorphic encryption (on addition modulo N) not based on prime factorization

A cryptographic function is homomorphic on some operation if that operation is preserved in the encrypted data. Such a function is homomorphic on addition modulo if the following holds for some ...
3
votes
1answer
87 views

What happens to quantum algorithms such as BB84 if P=NP

Under the hypothesis that P=NP, many cryptographic protocols are no longer secure (i.e. attacks are feasible). The BB84 algorithm (http://en.wikipedia.org/wiki/BB84) is based on the idea that by ...
3
votes
1answer
52 views

Iterative Byzantine consensus in directed graphs with unbounded malicious nodes

I've found many articles describing iterative procedures to reach Byzantine agreement on a graph (for instance http://www.crhc.illinois.edu/wireless/papers/icdcn14-vaidya.pdf or ...
5
votes
1answer
148 views

What is the complete version of the paper: “How to Generate and Exchange Secrets (extended abstract)” by Andrew Yao?

I've found numerous places that claim that the paper "How to Generate and Exchange Secrets" by Andrew Yao introduces garbled circuits as a solution to the secure multiparty computation problem. ...
0
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1answer
46 views

Finding the private key in BB84 quantum cryptography

I'm trying to teach myself Quantum Cryptography for an exam I have soon, and I came across the following question: To establish a common key, Alice and Bob analyse a sequence of 20 photon pairs. ...
2
votes
0answers
28 views

Proof of correctness of the XL-algorithm for polynomial systems

Section 12.4 of G.V. Bard's Algebraic Cryptanalysis discusses the XL-algorithm (first reported by N.T. Courtois and A. Shamir in Efficient algorithms for solving overdefined systems of multivariate ...
1
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1answer
146 views

RSA encryption why does ed=1?

So I fully understand the how the RSA algorithm works, but now I am trying to reason with the formula. I want to know: why the public key e and the private key d in the RSA encryption have to ...
7
votes
1answer
179 views

NP Problems with unique solution

Is there any class of NP problems that have one unique solution? I'm asking that, because when I was studying cryptography I read about the knapsack and I found very interesting the idea.
1
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2answers
114 views

In RSA, must $p$ and $q$ have the same number of bits?

Is it necessary to take the same bit size of "p" and "q" in case of RSA algorithm? i had read that bitsize of p and q must be same. BUT after calculating, i found that bit size could be different ...
8
votes
6answers
269 views

Could program verification techniques prevent bugs of the genre of Heartbleed from occurring?

On the matter of the Heartbleed bug, Bruce Schneier wrote in his Crypto-Gram of 15th April: '"Catastrophic" is the right word. On the scale of 1 to 10, this is an 11.' I read several years ago that a ...
5
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4answers
210 views

Can all NP-complete cryptosystems be broken if one is broken?

I was just reading something about NP-hard problems and cryptosystems. I was thinking: Every NP-complete problem can be reduced to another and every NP-complete problem has an equivalent (NP-hard) ...
0
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1answer
91 views

Finding prime factors of non-random key generator

I have been working on a challenge i found on the internet. It is as follows: You've stumbled onto a significant vulnerability in a commonly used cryptographic library. It turns out that the ...