Questions tagged [ntru]
NTRU is an encryption algorithm which is based on the shortest vector problem in a lattice.
2
votes
0answers
80 views
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)...
2
votes
1answer
87 views
Encrypt your ECDSA signature with NTRU to make them quantum secure, does that work?
I have a general question about quantum security. ECDSA is suppose to be broken by quantum computers. Whilst something like NTRU is suppose to be secure.
My question is: if we sign with ECDSA and ...
2
votes
1answer
68 views
Original NTRU : How to calculate the size of private key?
In the original NTRU paper：NTRU: A Ring-Based Public Key Cryptosystem,1996, the author proposes 3 choices of implementation parameters: moderate, high and highest. Let's take moderate security level ...
3
votes
2answers
122 views
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 ...
-1
votes
1answer
65 views
Decide whether a polynomial is invertible mod $q$
When implementing NTRU related cryptosystem, I came across the problem of deciding whether a randomly generated polynomial is invertible mod $q$. How to solve it?
0
votes
0answers
38 views
Can NTRUPrime public keys be identified from ciphertext?
Is it possible to distinguish which NTRU public key a ciphertext/encrypted message is for? Assume the attacker has no plaintext or access to secret keys.
I suppose this would be a form of key ...
0
votes
0answers
64 views
Multiplicative inverse for polynomial in NTRU encryption and NTRU attacks?
I know that we use EEC for calculate the multiplicative inverse but the problem to me is to calculate the inverse.
I mean if i have $f(x) = x^6-x^4+x^3+x^2-1$ and $(N, p, q, d) = (7, 3, 41, 2)$, ...
1
vote
1answer
93 views
Is there is a way to calculate the public key from the private key in pqNTRUSign algorithm?
There is source code of this algorithm (https://github.com/NTRUOpenSourceProject/NTRUMLS). But this algorithm does not provide a function for generating a public key from a private key. Studying the ...
3
votes
1answer
107 views
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: $e = e + pr \pmod q$ (...
1
vote
0answers
177 views
NTRUencrypt: why is it dangerous to use two different ephemeral keys for the same message?
I'm self-studying NTRU encrypt, and I read following in the book "an introduction to mathematical cryptography" -Chapter 6.10-remark 6.50 (Jeffrey hoffstein, Jill Pipher, Joseph H. silverman):
NTRU ...
2
votes
0answers
96 views
NTRU-based threshold encryption system?
I want to implement threshold homomorphic encryption for my project.
(encrypt a message using one public key, and decrypt a ciphertext using distributed secret keys)
I read a paper "Multiparty ...
2
votes
1answer
329 views
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 ...
5
votes
1answer
145 views
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 ...
-3
votes
1answer
124 views
Uniform Distribution and discrete Gaussian distribution for NTRU
I want to implement the NTRU cryptosystem. What is the method and algorithm to choose vectors elements from a uniform distribution and discrete Gaussian distribution?
2
votes
2answers
418 views
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 ...
1
vote
1answer
143 views
Explain: An NTRU key for a lattice of dimension $d$ has size only $O(d\log{d})$
The associated NTRU lattice is of dimension $d=2N$.
The public and private key sizes are both of length $O(N)=O(d/2)=O(d)$.
So where does the $d\log(d)$ appear?
Thanks in advance.
4
votes
1answer
519 views
NTRU Backdoor and New Hope TLS Protocol
The pre-print, Unstructured Inversions of New Hope was posted yesterday and uses a backdoor method against NTRU to claim that Grover's algorithm and an inversion oracle could be applied to New Hope.
...
2
votes
1answer
121 views
Message expansion in NTRU: why is it $\log_p(q)$-to-$1$?
Suppose that we are working with the original version of NTRU with parameters $(N,p,q,k,d_f,d_g,d_\phi)$.
In this case we are working with the original NTRU with the digital envelope and the ...
0
votes
1answer
79 views
In NTRU digital envelope, do everyone know the hash function $H$ used?
I have a simple question about the NTRU original cryptosystem using a digital envelope.
The article can be found here: http://grouper.ieee.org/groups/1363/lattPK/submissions/ntru.pdf
It is said that ...
4
votes
0answers
136 views
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 (...
5
votes
1answer
507 views
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 ...
2
votes
2answers
962 views
Calculating Polynomial Inverse with extended euclid in java
I'm trying to understand the NTRU-PKCS and therefor I wanted to code a naive Version of it. Now my Problem:
I tried to calculate the inverse of a Polynomial with an extended Version of euclids ...
4
votes
0answers
79 views
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 &...
2
votes
1answer
309 views
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?
7
votes
2answers
275 views
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 ...
0
votes
1answer
380 views
how to define the Truncated Polynomial?
In NTRUEncryption, I seen the trucated polynimials, but I cannot understand the trunacated polynomial calculation.
So, could tell me anyone How do we calculate the truncated polynomial?
4
votes
0answers
200 views
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 ...
7
votes
1answer
581 views
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 ...
2
votes
2answers
2k views
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 ...
6
votes
2answers
259 views
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 ...
4
votes
0answers
97 views
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 (...
0
votes
0answers
56 views
How do I check if the secret key polynomial of the ATV-FHE (NTRU based) scheme is invertible?
I want to implement the ATV-FHE scheme as described here https://eprint.iacr.org/2014/039.pdf. To generate the secret key polynomial I compute f = 2*u + 1 , with scheme parameters chosen such that ...
0
votes
0answers
29 views
What is the bound for the probability distribution for ATV-FHE scheme?
I try to implement the ATV-FHE scheme as described in this paper https://eprint.iacr.org/2014/039.pdf.
How do I choose the bound for the probability distribution chi?
How do I choose standard ...
1
vote
0answers
45 views
How to generate public key for ATV-FHE scheme?
I want to implement the ATV-FHE scheme as it is described here https://eprint.iacr.org/2014/039.pdf. How to generate the public key?
Should I compute it as indicated in section 2 :
$h(i) = 2g(i)*[...
3
votes
0answers
105 views
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 ...
0
votes
0answers
48 views
How to toggle a bit homomorphically ?
Suppose I want to use LTV scheme from this paper https://eprint.iacr.org/2013/094.pdf to compute homomorphically a function.
But the multiplication operation is more expensive than the additive one.
...
4
votes
2answers
185 views
Is reverse NTRU still secure?
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 ...
2
votes
2answers
196 views
What kind of operations are involved in NTRU?
I've read that lattice based algorithms involve matrix-vector products. Is this the case of the NTRU algorithm?
When I've read the details of the NTRU algorithm, I've seen products of polynoms. Where ...
6
votes
1answer
202 views
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 ...
3
votes
1answer
195 views
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 ...
2
votes
1answer
482 views
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 $\...
4
votes
1answer
778 views
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 ...
2
votes
1answer
565 views
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 ...
1
vote
1answer
389 views
NTRU Encryption
It's using Euclidian inverse. Can you show it step by step?
$$N=7, q=11, a = 3+2X^2 -3X^4 +X^6$$
the inverse of $a \pmod {11}$ is
$$A=-2+4X+2X^2 +4X^3 -4X^4 +2X^5 -2X^6$$
How do we compute $A$?
1
vote
2answers
411 views
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 ...
2
votes
1answer
200 views
Reduced message expansion in NTRU
In the original NTRU proposal from 1998, it says on page 16:
It may be worth mentioning, though, that there is a simple. masking technique that can be used to significantly reduce message expansion....
7
votes
1answer
637 views
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 ...
-1
votes
1answer
376 views
Convert message to polynomial NTRU
How to make a message into a polynomial? I saw many answers to this question and yes, i know that here are some questions. But i did not get it. I think that i am making some mistakes. I took a word ...
2
votes
4answers
609 views
Does NTRU provide Perfect Forward Secrecy?
Does NTRU provide Perfect Forward Secrecy if the world would use it in an HTTPS connection?
2
votes
0answers
131 views
How can I make a message into a blocks for NTRU?
I have more bits than the degree of the NTRU polynomial.
For example: $x^{11}-1$
message: Hello (I am using ascii, 8 bits for 1 symbol)
got: ...
