Questions tagged [ntru]
NTRU is an encryption algorithm which is based on the shortest vector problem in a lattice.
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Does NTRU decrypt correctly now?
The NTRU public-key cryptosystem has a lot of interesting properties (being resistant to quantum computer attacks, being standardized by several important bodies), but it also has a pretty unique ...
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Which attacks are possible against raw/textbook NTRU encryption?
In the same fashion that these questions about attacks to textbook RSA and ECC, I was wondering what are the immediate drawbacks of applying NTRU Encryption directly, without any padding scheme, such ...
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How can one sign with NTRU?
I am looking at implementing NTRU, but I noticed that while the encryption/decryption algorithm seems to be mature and well-documented, there is comparatively little information about how to sign ...
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Secure, patent-free alternative to NTRU
I'm working on a P2P communications and chat framework, and am looking for a quantum-secure asymmetric key exchange algorithm which I can use to perform a key exchange of an AES-256 bit key. This is ...
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Why does NTRUEncrypt lack a formal security proof?
Is there any particular reason why NTRUEncrypt lacks a formal security proof? That is, a demonstration that it achieves certain security notion (e.g. IND-CPA). I know there is a provable-secure ...
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Multiple NTRU public keys for the same private key?
An NTRU public key is generated essentially by multiplying the inverse of a polynomial $f$ by a polynomial $g$. The polynomial $f$ is the private key; $g$ is discarded.
My question is: Is it insecure ...
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NTRU crypto from unseen.is; myth busting help
I am always on the look out for privacy enhancing technologies. I stumbled upon the service from unseen.is. I had a look at their site (specifically here) and even though I lack knowledge there are a ...
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NTRU Cryptosystem: Why "rotated" coefficients of key f work the same as f
In the NTRU cryptosystem, we can use a randomly generated polynomial f that is inversible under modulo p and q to encrypt and decrypt our plaintext. While studying this system, I attempted to ...
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Implementations of Ntru TLS
Has anyone come across any implementations of Ntru TLS? I'm working a project for uni that does quantum secure encryption. It relies on a mix of Ntru & AES, but I can't find an implementation of ...
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What is the most efficient attack on NTRU?
So, I got how finding the private key is equivalent to resolving the SVP. I also understood that the LLL algorithm can only be used in small dimensions. Now, I wonder what is the most efficient attack ...
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Layered encryption in mixnets with post-quantum cryptography
I am trying to implement a mixnet using post-quantum public-key crypto. Each message may be encrypted by up to 10 levels of public keys, shuffled, before the layers of encryption are stripped off one ...
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Where can I find NTRU test vectors?
In some research work in 2001, it is stated that test vectors were not publicly available at the time. Then in this ESSS1v2 standard under IEEE1363 here , the appendix B mentions that the test vectors ...
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Does NTRU provide Perfect Forward Secrecy?
Does NTRU provide Perfect Forward Secrecy if the world would use it in an HTTPS connection?
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NTRUencrypt in NIST competition
Why did the NTRUencrypt team not maintain the NTRU1024 release in the NIST second-round competition?
Is this because of the speed performance or security performance or other things?
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NTRU key size (confused)
I'm evaluating the performance of NTRU; and I got confused. the key size is said to be smaller than RSA but larger than ECC.
Using both the reference implementation when I choose APR2011_439 setting ...
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NTRU Backdoor and NewHope TLS Protocol
The pre-print, Unstructured Inversions of NewHope was posted yesterday and uses a backdoor method against NTRU to claim that Grover's algorithm and an inversion oracle could be applied to NewHope.
My ...
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Is reverse NTRU still secure? (Looking for a signature scheme)
I'm currently prototyping something with the NTRU encryption scheme but I wish to use it in "reverse" -- distribute private keys so anyone can decrypt, but keep the public keys secret and thus only ...
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Lightweight Asymmetric encryption algorithm
I'm an embedded systems researcher, and new in the crypto field. Actually, I need to know if there are any lightweight asymmetric encryption algorithm especially considering the time needed for key ...
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Inverses in Truncated Polynomial Rings
I've been trying a long time to understand a thing which is obviously extremely simple, but I just can't get it.
Read this, please:
The NTRUEncrypt PKCS uses the ring of truncated polynomials $R$ ...
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what are the NTRU keysize and application in industry?
I'm a student currently working on a research project on the NTRU cryptosystem, I've read some papers about this cryptosystem, and in those papers they are talking about keysize, is it the size of the ...
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Is NTRU still hard if $G$ is set to 1?
I'm looking at the description of NTRUEncrypt given on page 21 of http://archive.dimacs.rutgers.edu/Workshops/Post-Quantum/Slides/Silverman.pdf and using its notation. So in NTRU there are always two ...
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NTRU less secure than previously thought?
A new paper (https://eprint.iacr.org/2015/552.pdf) says:
This makes it possible to asymptotically and heuristically break the NTRU cryptosystem in subexponential time (without contradicting its ...
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What is the NTRU parameter equivalent to security level 112, 128 and 192?
I came across this paper which mentions this table, which states that NTRU 347 is equivalent to 112 bit security level
However, in this paper, Choosing parameters for NTRU mentions that NTRU-401 is ...
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What is the largest parameter broken for NTRU?
The original secure parameters for NTRU shown below are from the original HPS98 paper. This is vastly different from the current secure suggested parameters in the NIST PQC round 3 submission.
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How can I implement decryption for NTRU homomorphic encryption scheme?
I have come across this paper On-the-fly multiparty computation via on-the-cloud Multikey from Fully Homomorphic Encryption by Lopez-Alt et al., where authors describe a NTRU-based homomorphic ...
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How about a homomorphic integer sorting in a MPC context?
I want to implement the ATV-FHE scheme as described by Adriana López-Alt, Eran Tromer, Vinod Vaikuntanathan: On-the-Fly Multiparty Computation on the Cloud via Multikey Fully Homomorphic Encryption (...
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Is the combination of X25519 ECDH and NTRU in OpenSSH 9.X secure against quantum attacks?
Can the combination of X25519 ECDH and NTRU in OpenSSH 9.X defend me against quantum attacks?
Why is it believed that this combination is secure?
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Is the IEEE 1363.1 standard of NTRU post-quantum secure?
I have a question regarding the IEEE 1363.1 standard for NTRU with padding, which offers CCA security. Does the IEEE standardized implementation offer post-quantum security as well?
Also, what are the ...
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How to decide if an element is a public key in NTRU encryption scheme?
First, I'm using the settings of https://en.wikipedia.org/wiki/NTRUEncrypt, with $L_f$ set of polynomials with $d_f+1$ coefficients equal to 1, $d_f$ equal to $-1$ and the remaining $N-2d_f-1$ equal ...
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NTRUEncrypt fails on sedonion algebra
This question is a direct follow-up (hopefully - the last) of my previous one; please see it for full information. I would like to further generalise NTRU cryptosystem on higher-order algebras. ...
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How to find the inverse of a polynomial in NTRU-PKCS
I am coding a java based implementation of the NTRU public-key cryptosystem. I can comprehend the majority of the algorithms involved in the encryption and decryption process well enough, but the key ...
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NTRU and one failed example
In NTRU crypto system I have used these polynomials and parameters:
$N = 17, p = 7, q = 64$ and $f$ as private key is:
$$f = -1 + x + x^2 - x^4 + x^6 + x^9 - x^{10}$$
So the inverse of $f$ in ring $\...
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Illustrate NTRU using lattices
I studied some papers related to NTRU. All these papers describe NTRU as a lattice based cryptosystem but I could not find any paper which illustrates NTRU algorithm from lattice point of view. It ...
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Do ideal non-cyclotomic lattices provide better compression in lattice-based cryptography?
Let $f \in \mathbb{Z}[x]$ be an irreducible polynomial of degree $N$ and $q \in \mathbb{N}$. Consider the rings $R := \mathbb{Z}[x]/f$ and $R_q := R/q$. Obviously, an element of $R_q$ can be ...
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Regarding NTRU homomorphic properties
NTRU has some homomorphic properties modulo q, supporting both addition and multiplication. Due to its nature, it cannot support many of them. My main focus currently is in the addition, so the ...
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Are high-dimensional versions of NTRU cryptosystem more secure?
The basis for this question is a 1-dimensional NTRU cryptosystem.
After some literature inspection I have found out it can be also generalised into higher algebras: quaternions (QTRU) and octonions (...
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Is Ntru-Encrypt still secure in 2022
I'm going to use NTRU as post-quantum public-key encryption algo in my project.
I've googled attacks on NTRU and found a lot of them
but since I'm new to NTRU and don't understand the math used, and ...
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Coppersmith attack on NTRU and non-commutativity
In this paper, Coppersmith and Shamir used lattice reduction to attack NTRU. At the very end of the paper, they note that developing non-commutative variants of NTRU would be wise, in light of their ...
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Comparison of NTRU-based schemes and LWE-based schemes
What advantages and disadvantages can be distinguished in NTRU-based and LWE-based schemes relative to each other? In what cases which scheme gives advantage?
UPD: I'm interesting in two things: 1)...
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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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On a proposition in NTRU original paper: $\gamma_1 |f|_2 |g|_2 \leq |f \circledast g|_\infty \leq \gamma_2 |f|_2 |g|_2$
In the original paper of NTRU cryptosystem, we have the following proposition (that is said to be suggested by Don Coppersmith):
For any $\epsilon > 0$, there are constants $\gamma_1,\gamma_2 &...
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How to test a FHE implementation?
I want to implement a FHE scheme based on NTRU, namely the scheme described here https://eprint.iacr.org/2014/039.pdf . How to test the security of my implementation ? Do I have to implement the ...
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How to make a message into a polynomial on NTRU encryption?
How to make a message into a polynomial on NTRU encryption? for example how we can conver 'hello world' to polynomial...
i have read the converting operation on IEEE Std 1363.1- 2008, but i can't ...
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Dense sphere packings and lattice-based cryptography
It is known that there are two popular applications of lattices: dense sphere packings and lattice-based cryptography. I didn't find any information on the Internet about possible interaction of these ...
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NTRUEncrypt fails on quaternion algebra
This is a follow-up of my previous two questions (1 and 2), might be relevant to check them out first for a full context. I am trying to re-create results from this paper. The basic algorithm is ...
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Volume of an NTRU lattice
Let $K$ be a number field of degree $n$ and $\Lambda^q_h=\{(f,g)\in\mathcal{O}_K\text{ : }fh-g = 0\bmod q\mathcal{O}_K\}$, where $h$ is an NTRU public key. Then $\{(1,h),(0,q)\}$ generates a lattice. ...
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NTRU homomorphic rerandomization
I am currently implementing NTRU, keeping its homomorphic properties. I want to implement rerandomization like this:
Encryption: $e = pr * h + m \pmod q$
Rerandomization: $e = e + pr \pmod q$ (...
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Key and signature sizes of NTRU and NTRU Prime?
I would have expected this info to be easier to Google Scholar for, but alas I'm asking here.
Partial answers:
NTRU key size (confused)
the public key consists of one ring, and so it takes up $11 ...
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What is the most common encoding of messages to polynomials?
How polynomial based encryption schemes such as NTRU encode messages in to polynomials? Is there a generic conversion?
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NTRU key generation
I've been experimenting with an NTRU open-source C implementation here
I've noticed something (potentionally) strange with a certain set of params: NTRU_EES1087EP2 (defined here).
When generating ...
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