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Questions tagged [cr.crypto-security]

Theoretical aspects of cryptography and information security.

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Attacks on Niederreiter cryptosystem

Guo et al presented an attack on QC LDPC McEliece cryptosystem. Before that, a similar attack was presented on QC MDPC in Asiacrypt by Guo et al. Do these attacks also work on Niederreiter ...
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PPAD and Quantum

Today in New York and all over the world Christos Papadimitriou's birthday is celebrated. This is a good opportunity to ask about the relations between Christos' complexity class PPAD (and his other ...
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Quantum security of cryptosystems

One of the main candidates for PQ cryptography is code based cryptography (other than lattice based). The Niederreiter cryptosystem based on goppa codes is shown to be resistant to hidden subgroup ...
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Underlying codes in Niederreiter cryptosystems

Niederreiter cryptosystem is usually described by a parity check matrix $H$ over $\mathbb{F}_{2^n}$. The minimum distance $d$ is given by $d= min\lbrace k \text{ such that there are $k$ linearly ...
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If I know pretty well '(a,b)', I know pretty well 'a', or 'b', or 'a xor b'

I've a quite simple problem: let's imagine I have a couple of bits $(a,b) \in \{0,1\}^2$ sampled uniformly at random. Then, I give a function of these bits $f(a,b)$ (it can be any function, including ...
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Would an NP-complete public key cryptosystem imply NP=co-NP?

Would the existence of an NP-complete (or co-NP-complete) public key signature cryptosystem imply that NP = co-NP? My specialty is definitely not theoretical computer science, so this is somewhat of ...
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Cryptography protocols using graph problem instances

I personally am only aware of basic examples of public key cryptography and I haven't studied cryptography yet. I'm curious if there are circumstances in cryptography where using problem instances ...
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What is the state of the art in online voting?

Is there a cryptographic protocol which, at least in theory (and under standard cryptographic assumptions) enables people to securely vote from their homes? I could see how the various problems might ...
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Password hashing using NP complete problems

Commonly used password hashing algorithms work like this today: Salt the password and feed it into a KDF. For example, using PBKDF2-HMAC-SHA1, the password hashing process is ...
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207 views

Which cryptographic protocols are secure against quantum computer attacks?

Are there any cryptosystems that we know that would be secure against an attack by a quantum computer? Are there problems which are known or suspected to be hard for quantum computers, and can these ...
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How hard is it to generate a set of relatively prime numbers between two given bounds?

Informal Question How hard is it to generate a set of relatively prime numbers between two given bounds? Decision Problem Given $a$, $b$, and $k \in \mathbb{N}$. Does there exist a set $S \...
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Is it possible to encrypt a CNF?

Is it possible to convert a CNF $\mathcal C$ into another CNF $\Psi(\mathcal C)$ such that The function $\Psi$ can be computed in polynomial time from some secret random parameter $r$. $\Psi(\mathcal ...
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Can any computational challenge be transformed to proof-of-work?

The seemingly pointlessness of cryptocurrency mining raised the question of useful alternatives, see these questions on Bitcoin, CST, MO. I wonder whether there exists an algorithm that can convert ...
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Can entropicly secure encryption algorithms be used on low-entropy messages by adding noise

There exist information-theoretic notions of security like Shannon's "perfect security" that one-time pads exhibit. All methods which achieve perfect security will require long keys, however. If we ...
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Is there a fast algorithm to quickly evaluate $a^{b^c}$ mod $n$?

I need to quickly evaluate $a^{b^c} \mod n$ where $c$ is pretty big. Using the usual repeated squaring trick, this can be performed in $O(\log(b^c)) = O(c)$ time. In my problem, $c$ is huge, (say, $&...
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Why is the security of lattice cryptosystems not provable from $P \neq NP$?

My understanding is that the Shortest Vector Problem ($\text{SVP}$) is $\text{NP}$-hard. Therefore, $\text{LWE}$ is also $\text{NP}$-hard. But $\text{LWE}$ is hard on average if it is hard in the ...
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Problems equivalent to the existence of secure cryptosystems? [closed]

What are some necessary and sufficient conditions for the existence of following? Symmetric encryption (defined here as satisfying $\text{IND-CPA}$ and $\text{INT_CTXT}$) Asymmetric encryption ...
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“Security Against Covert Adversaries” question

I was reading the paper Security Against Covert Adversaries: Efficient Protocols for Realistic Adversaries by Aumann and Lindell, and had some questions with the protocol for covert OT given errorless ...
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Is [2-party d3-rolling with maximum probability 1/2] known to imply one-way functions?

Most things in complexity-based cryptography (for examples, see page 4) are known to imply the existence of one-way functions, especially after this paper proved that implication for weak coin-...
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The factoring problem reduces to order finding or is it the other way around? [closed]

initially i was not at all equipped in theoretical computer science and knew only basics of number of theory. I started working from scratch on the age old problem of primality testing which led me to ...
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4answers
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Is a theoretically secure key exchange possible?

During a discussion I was wondering if it would be possible to design a theoretically secure key exchange. In other words: If it is possible to design a key exchange (like Diffie–Hellman) where the ...
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Can a random oracle change which TFNP problems are strongly hard-on-average?

I've been thinking about the following question at various times since I saw this question on Cryptography. Question Let $R$ be a TFNP relation. ​ Can a random oracle help P/poly to break $R$ ...
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Is a “complete” cipher possible?

Is a "complete" symmetric cipher possible? By this I mean a symmetric cipher that is provably secure under the assumption that a secure symmetric cipher exists.
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Is it possible to MAC a quantum state with a classical key under reasonable assumption?

Assume that classical one-way functions secure against quantum adversaries exist. Is it possible, given a quantum state $Q$ and classical secret key $k$, produce a quantum state $AuthQ$ such that: ...
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Is it possible to encrypt quantum states under reasonable assumptions?

Is it possible to encrypt a quantum state, such that a $BQP$ attacker who does not know the secret key cannot obtain any information about the original state, but a $BQP$ decryptor with the key can ...
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Does Factoring have a Statistical Zero Knowledge Proof?

The title should be pretty self-explanatory, but to be more precise, consider the decision version of factoring, which is given input $(x,k)$, where $x$ and $k$ are binary encodings of integers, to ...
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Quantum algorithms for generalizations of determinants

There are a wide variety of determent-like constructions. Some like the permanent or immanents are variations on the ordinary determinant for matrices over fields or commutative rings. Some like ...
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How to find a non-zero point of a non-zero polynomial of low degree?

Given a circuit that computes a polynomial $P(x_1 \dots x_n)$ of low formal degree over some large field $\mathbb{F}$. Moreover, given a point $X \in \mathbb{F}^n$, such that $P(X) \neq 0$. Can one ...
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Quantum Hardness of Approximating Lattice Problems

A common claim in lattice-based cryptography is that cryptosystems based on the Learning with Errors ($\mathsf{LWE}$) problem are hard to break (for a per-system definition of "break") for quantum ...
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Quantum Hardness of Finding Nash Equilibria

This question is inspired by the recent, beautiful work On the Cryptographic Hardness of Finding a Nash Equilibrium by Bitansky, Paneth, and Rosen. Their main result is that the existence of ...
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508 views

Alternatives to Diffie Hellman

Assume that Discrete logarithms can be solved in linear time over any group (hence factorization is also trivial by a result of Eric Bach), is there any other candidate public key exchange problem ...
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Complexity classes for proofs of knowledge

Prompted by a question Greg Kuperberg asked me, I'm wondering if there are any papers that define and study complexity classes of languages admitting various kinds of proofs of knowledge. Classes ...
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Knot Recognition as a Proof of Work

Currently bitcoin has a proof of work (PoW) system using SHA256. Other hash functions use a proof of work system use graphs, partial hash function inversion. Is it possible to use a Decision problem ...
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Extractor with somewhat corrupted seeds

In conditional min-entropy extractor, there is a joint distribution $(X,Y)$ such that if the average min-entropy (for some appropriate notion of it) ${\rm H}_\infty(X|Y)$ is large, then ${\rm Ext}(X, ...
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134 views

Factoring semiprimes whose factors very close to a power of two

Are there any factorization algorithms that run well on numbers $N = pq$ where $p,q$ are prime and $p = 2^b - k_p, q = 2^b - k_q$ for very small $k_p,k_q$? What about $p = 2^b + k_p, q = 2^b + k_q$ ...
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Claw finding using quantum walk: superposition for Szegedy's framework

Within Claw Finding Algorithms Using Quantum Walk there is the subroutine $claw_{detect}$ described. As in above paper: Let $J_f(N, l)$ and $J_G(M, m)$ be Johnson graphs. Let $F$ and $G$ be vertices ...
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204 views

Information-theoretic Diffie-Hellman

The following non-standard description of Diffie-Hellman is entirely my own, by which I mean that I came up with it having not read about it anywhere else beforehand. In Diffie-Hellman Alice and Bob ...
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Can we construct a k-wise independent permutation on [n] using only constant time and space?

Let $k>0$ be a fixed constant. Given an integer $n$, we want to construct a permutation $\sigma \in S_n$ such that: The construction uses constant time and space (i.e. preprocessing takes ...
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Simple candidates for pseudorandom permutations?

Even though it is not known whether one-way functions exist, there are several candidate functions used in practice for cryptographic applications that are efficiently computable but are conjectured ...
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Question on cryptographic advantage

In Provably Secure Steganography by Hopper, et al, we have the following definition Cryptographic notions Let $F:\{0,1\}^k \times \{0,1\}^L \rightarrow \{0,1\}^l$ denote a family of functions. Let $...
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Introductions to steganography from an information-theoretic standpoint

Can I get some introductory references for steganography from an information-theoretic standpoint? I recently listened to a talk on it, and the speaker said that he knew of no good introductions to ...
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1answer
154 views

Cryptography with very small keys

Is anything known about doing cryptography with very small keys? In particular, is there any theory involving cryptosystems (based on whatever assumption you want) that can encrypt messages of length ...
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One kind of dependence relation between a pair of random variables

I have been working on privacy and come across a neat problem. Suppose two random variables $X$ and $Y$, over finite alphabets $\mathcal{X}$ and $\mathcal{Y}$, are given with joint distribution $P_{...
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Cryptographic systems that don't leak linear combinations of encrypted bits

Various encryption schemes would be considered broken if an adversary could have a non-negligible edge in predicting the first (or any) bit of an encrypted message. I am looking for a slightly ...
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185 views

Reference on cryptography methods

I'm looking for a good reference, possibly a survey, on the different types of cryptography methods. As far as I understand, the security of a cryptographic method depends on some hardness assumptions,...
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Is it possible to encrypt something in such a way that it can be decrypted by two different keys?

I'm a lowly web dev / programmer of 10 years who's never tried to wrap his brain around the high concept stuff, so apologies is this is a stupid question (or if it belongs in programmers.stackexchange....
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Is it possible to make trapdoor board games?

Motivated partly by this MO question, I am wondering if it's possible to design a board game where there is a simple winning strategy but it's hard to find. For example, the game of picking a random ...
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Why does most cryptography depend on large prime number pairs, as opposed to other problems?

Most current cryptography methods depend on the difficulty of factoring numbers that are the product of two large prime numbers. As I understand it, that is difficult only as long as the method used ...
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Understanding the weak-OWF exists -> OWF exists proof

This is a proof that I've gone back to many times over the last few years and while I can read it and easily verify the steps, it seems like it's a proof, where I will always essentially forget the ...
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1answer
179 views

Efficient Shamir secret sharing reconstruction

Shamir's secret sharing scheme is a well known way to convert a secret into a polynomial and distribute points in this polynomial. Some of these points can then be regrouped to reconstruct the ...