Questions tagged [public-key]

An asymmetric cipher is an encryption scheme using a pair of keys, one to encrypt and a second to decrypt a message. This way the encrypting key need not be kept secret to ensure a private communication. Similarly in public key authentication, the verification key can be public and the signing key private.

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Given a 'good' basis for a lattice, how can we solve the CVP?

I'm doing a little bit of reading about lattices. I read that if we can find a 'short' basis for our given lattice, we can solve CVP and SVP very efficiently. However, the paper didn't describe an ...
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Zero knowledge proof for Paillier addition under multiple keys

Suppose $m_0, m_1, m_2 \in \mathbb{N}$ such that $m_0 = m_1 + m_2$, $m_i > 0$ (none of them can be 0 or lower) Under a Paillier cryptosystem, set $e_0 = E(m_0, r_0)$ for a public key $(g_0, n_0)$ ...
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Is qTesla Secure?

qTesla is a signature scheme and a submission to the NIST post-quantum standardization process, which made it to the second round. It is based on the hardness of RLWE. The NIST round 2 status report ...
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What public-key encryption protocol can use the same key pair as ECDSA?

Assume we wanted to use the same ECDSA public/private key pair (drawn for standard ECC parameters, perhaps P-256) for both its intended use (public-key signature), and for public-key encryption; this ...
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MuSig: could the rogue key attack be mitigated by using commitments instead of key transformations?

Background MuSig is an extension of/derivation from Schnorr signatures using cyclic groups on elliptic curves. In the original paper, the authors point out that naive multi-Schnorr is vulnerable to a ...
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Cryptomania and NP $\cap$ co-NP

Cryptomania is usually presented as the Impagliazzo's world, which gives us public-key cryptography under the assumption that trapdoor OWFs exist. For purposes of constructing public-key cryptography ...
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Help with cryptanalysis of branching in schemes based on Multivariate Public Key Cryptography

I'm familiarized with the structure of branching found in Multivariate Cryptography, as it allows us to partition a $n$-tuple over $F_{q}$ into a $k$-tuple where the $i$-th element is in $F_{q^{\...
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Generalized Benaloh cryptosystem with $r=2$

Benaloh cryptosystem requires $\gcd(r, (q-1))=1$ which is impossible if $q>2$ (since it needs to be a large prime) and $r=2$. This confuses me, since Benaloh is referred to as an "extension" or "...
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Where do the PKs come from in Bluetooth device?

I am studying the Elliptic Curve Diffie-Hellman (ECDH) on Bluetooth 4.2. There are some questions about the PK.. Where do these public and private keys come from? Who defines them? and Will it be ...
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Public key encryption from (1,2)-oblivious transfer

Prove that any two rounds of (1,2)-oblivious transfer, that is semi honestly secure, imply public key encryption. My ideas so far: Let's say Alice samples two $n$ random strings $(x_1, x_2)$, and ...
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Why is this scheme not IND-CCA2 secure

I know that many lattice cryptosystems cannot be made $\text{IND-CCA2}$ or even $\text{IND-CCA}$ secure without substantial overhead. However, it seems that (when used as a KEM) that any $\text{IND-...
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How did G.H. Hardy's work contribute to today's public-key cryptography?

I know that Hardy's work in number theory was used by Clifford Cocks in 1973 to develop the basis for public-key cryptography. What specifically was this work, and how is it used today in ...
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Is it possible to have a shared secret without any party knowing all the parts?

I believe with Shamir’s Secret Sharing Scheme, I can create an n-part secret and distribute each of those parts to n parties. ...
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Have time-release servers been implemented?

Conceivably, Alice could release a public encryption key and promise to release the private decryption key on a certain date. That way anyone could use that encryption key, combined with others from ...
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Key strength comparison: symmetric key vs RSA/DH key

I came across different reputable sources quoting different equivalent symmetric key strengths for RSA/DH keys. This NIST paper (page 67) states the following offer corresponding security strenghts (...
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Solving LPN using algorithm for syndrome decoding

Given an algorithm $A_D$ which solves an instance of the decoding problem $e \in \mathbb{F}_2^n$ in time $T_D$ given a parity check matrix $H \in \mathbb{F}_2^{(n-k)\times n}$ and a syndrome $s \in \...
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Encryption scheme that requires fewer keys for decryption than for encryption

I want to attempt creating a decentralized dead man's switch, so I'm looking for an asymmetric encryption scheme, with the following properties (ideally), or something close to them: There is a group ...
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Is it possible to verify attributes of encrypted content?

Let's say that Alice has this information about her, { "name": "Alice", "age": 25, "eyes": "brown" } which she encrypts with a key pair so that no one access ...
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How does the key agreement process take place in Virgil E3Kit SDK for end to end encryption?

I'm using Virgil E3Kit SDK to implement end-to-end encryption in my App. Their E3Kit SDK is very effective and not too hard to understand, but I still don't understand how does the key agreement ...
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3 votes
2 answers
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Revoke a GPG key using previously generated revoke certificate after renewd (change expiration date)

I have few sub-questions Do secret keys get expired, or just the public key gets expired? Do I have to back up the master sec key each time I renew it? For an ...
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How to define a FHE scheme whose plaintext space is infinite using boolean circuits?

There are many kinds of fully homomorphic encryption scheme by using boolean circuits. And the plaintext space $\mathcal{P} = \{ 0,1 \}$. If there is a -bit FHE scheme, we can construct a FHE scheme ...
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Montgomery modular multiplication – confusion with subtraction of modulus

I'm reading the paper “COMPARISON OF SCALABLE MONTGOMERY MODULAR MULTIPLICATION IMPLEMENTATIONS EMBEDDED IN RECONFIGURABLE HARDWARE” (PDF) on hardware algorithms for montgomery multiplication for ...
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RSA - factorizing $N$ to get $p$ and $q$

I need to decrypt a message encrypted using RSA. I only know the public keys $n$ and $e$. I need to get the private key $p$ and $q$ in order to get the decryption exponent $d$. Now to do so, I know ...
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In NTRU, if $N$ is not prime, prove that one can recover the private key by solving a lattice problem in dimension lower than $2N$

In the NTRU cryptosystem, it is suggested to take $N$ prime. I want to understand why. In Jeffrey Hoffstein, Jill Pipher and H. Silverman An Introduction to Mathematical Cryptography, they suggest (...
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David Chaum's anonymous credential

I am a newbie in cryptography (I know the basic RSA, AES stuffs) and am interested in anonymous authentication systems. Looks like David Chaum is the godly figure in the field. I see lots of people ...
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Why gcd(r,(p-1)/r) needs to be 1 in benaloh cryptosystem

I recently discovered the benaloh cryptosystem. I am working with the system as it is discribed in the following link: https://en.wikipedia.org/wiki/Benaloh_cryptosystem However I need some help in ...
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Is it possible to use PGP subkeys in multiple emails without correlating them?

I would like to know if sub-public keys of PGP keys can be published separately, if I create a pair of master keys and multiple sub keys to be used in multiple emails, and normally use only the sub ...
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2 votes
1 answer
249 views

What is the difference between the Fully Homomorphic BFV and BGV schemes?

When I read about BFV or BGV, they all look similar: they use polynomials from $\mathbb{Z}[X]/X^n+1$ as secret keys/pubic keys, etc. What is the main difference?
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How to convert plaintext to element of cyclic group in Cramer-Shoup cryptosystem

I am trying to implement a cramer-shoup cryptosystem but I don't understand how to work with the plaintext I want to encrypt. From what I understand, the plaintext needs to be converted to an element ...
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Why is asked that gcd(pq,(p-1)(q-1))=1 in the Paillier encryption scheme?

I don't see this property $\gcd(p\,q,(p-1)(q-1))=1$ used in the scheme. And in Paillier's original paper, I don't find this requirement. Is it required just for the difficulty of factoring $n$? Or is ...
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2 votes
2 answers
170 views

Combined scheme security proof

Let CS be a combined scheme of $n$ public key subschemes. CS is composed of two algorithms Setup and KeyGen, that all the subschemes share, plus all the other algorithms of each subscheme. Suppose ...
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What grade of protection does a private key's passphrase provide at best?

Does a passphrase with high entropy provide the same level of security as the private key itself? General scenario: An attacker has access to a private key file that is protected with a passphrase ...
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DES decryption of the homomorphic encryption ciphertext

I implemented an application using partial homomorphic encryption for outsourced computations. To get an efficient bandwidth, I am thinking to apply (DES) symmetric algorithm to encrypt the message ...
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2 votes
2 answers
251 views

Code used for McEliece cryptosystem

In the McEliece cryptosystem, is choice of the code known to the attacker? And if a structural attack succeeded and the attacker found the generator matrix of the code, how did the attacker decode the ...
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Fixed point in RSA encryption

Some papers count the number of the fixed points in the RSA encryption algorithm. They're a minimum of 9 and the real number depends on the smoothness of primes $p$ and $q$. It very unlikely that a ...
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Is the first Nonce exchange between Alice and Bob in Needham-Schroder key exchange protocol redundant?

For the Needham-Schroder protocol, assuming Alice and Bob are both able to guarantee each other's public keys (e.g. through a Certificate authority), the protocol is 1) A sends to B: $E_{publicB} [...
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Verifying the ownership of curve25519 public keys

Let's say we have a group of users, authenticated by a server that providers the service, communicating on a secure channel (e.g. over HTTPS/TLS) and each user has a corresponding curve25519 key pair. ...
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What are some examples of out of bound channels that work over the Internet in practice?

If I want to verify a public key (be it RSA, PGP, etc.) with another client over the Internet only, what are some viable out-of-bound channels for verification? Which channels have been used in ...
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Recursive RSA encryption

I have a ciphertext $C$ encrypted with public key $pub_C$, which contains ciphertext $B$ and $pub_B$, $$C= E_{pub_C}(B\mathbin\|pub_B)$$ Ciphertext $B$ is encrypted with $pub_B$ and contains $pub_A$ ...
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2 votes
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Verify commitment C commits to the same value that E encrypts

Given the following (using additive notation): $G$ - generator of an elliptic curve group of order $q$ $s$ - secret drawn uniformly from the distribution $1..q$ $k$ and $K$ - a private public keypair ...
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Homomorphic Public/Private Key Encryption Scheme for Floating Numbers

Is there any public/private homomorphic encryption scheme that directly works on floating numbers or vectors of floating numbers? In our application, we want to find out if $$v_1 \approx v_2, \qquad\...
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Asymmetric encryption, multiple recipients, traitor must share private key

Is there an asymmetric encryption scheme, or public-key encryption, where multiple recipients can access the data, but in order for one of the recipients to leak the key to the data, they would need ...
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A proposal for randomization of Niederreiter cryptosystem

The Niederreiter cryptosystem is a public key cryptosystem using Goppa code. Unfortunately it it is insecure unless it is a binary code. So I thought I could insert random linear codes into randomly ...
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2 votes
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Security of an Elliptic Curve Public Key with a "Small" x-coordinate

Consider an elliptic curve over a finite field $F_p$ with $p$ prime and order $n$. Let $Q$ be a generator for the field. Given a public key point $P = aQ$, suppose we have an algorithm that finds an ...
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How do pairings behave on G2/twist points off the prime order subgroup?

$\newcommand{\F}{\mathbb{F}}$ Consider the ate pairing defined on a curve $G_1 = E(\F_q)$ and $G_2 = E'(\F_{q^r})$ where $E'$ is a twist of $E$ with the twisting isomorphism defined over $\F_{q^r}$. ...
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Quantum Resistant Algorithms and types: PKE vs PKEs vs KEM vs KEMs vs DSS

I am trying to wrap my head around the second round Quantum Resistant Algorithm candidates currently under the NIST PQC Effort. Can someone verify if the following is a correct summary of the 17-...
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Derivable encryption key - BIP0032 parallel

I wish to find an asymmetric encryption algorithm that supports key derivation, BIP0032 style. Meaning that I have some SEED [PRIV] and I give someone some public data [PUB], then given new public ...
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Concept for a RSA "repeater". Is it sensible?

I have been using RSA signed/encrypted mailing a lot recently. Naturally, I wanted to use RSA mailing also on my phone, not only on my computer. However, I feel uneasy having my private key on my ...
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GPG Sub Key Renewal Questions

Last year, I followed this guide to create two GnuPG Smart Cards; one card with the Primary Key and the other card with the Sub-keys. I noticed that the sub keys were close to expiring so I renewed ...
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2 votes
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What standards of ECC point compression exist?

The method that I used before to decode EC point from public key led me in a dead end. So I just want to know what yet I could try. I've got a public key that I don't know how to decode and I am ...
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