Questions tagged [rlwe]

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67 views

Trying to Understand Ring Learning With Error Encryption

I'm trying to understand the following RLWE encryption scheme from this Chris Peikert's paper Say i choose $q = 97$, $n=8$ and the polynomial $a = 96 x^8+30 x^7+76 x^6+12 x^5+57 x^4+77 x^3+70 x^2+49 ...
2
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1answer
47 views

RLWE decision to search: probability that oracle work on all automorphic images

After watching this talk https://www.youtube.com/watch?v=Eg_pyyeT_Qc&feature=plcp, I tried to formalize the presented search-to-decision reduction for Ring LWE, but got stuck at one point. I ...
2
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1answer
70 views

Threshold decryption in multi-key homomorphic encryption

I have a problem understanding the security of threshold decryption in multi-key homomorphic encryption (MKHE) with so called "noise flooding". In particular I think that it is not secure, so probably ...
2
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1answer
54 views

Does the relationship between plaintext and ciphertext moduli affect the security of BGV/BV SwHE?

The SwHE schemes due to Brakerski and Vaikuntanathan (BV) and Brakerski-Gentry-Vaikuntanathan (BGV) have common concept in which the message bit is put in the least significant bit of the ciphertext. ...
2
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0answers
49 views

ZKPoK for RLWE secret and error

I came across How to validate the secret of a Ring Learning with Errors (RLWE) key paper by Ding et al., which seems to provide a ZK proof that the given $p$ is of the form $as + e$ with $s, e$ small ...
1
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1answer
61 views

How are precision and security related in a Gaussian Noise Sampler for R-LWE?

My understanding is that the sampling precision in Gaussian Noise sampler is related to security. But not sure about why is that? I read that when the samples are floating-point numbers and precision ...
0
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0answers
31 views

An example of calculation of BGV encryption

Can anyone give an example RLWE BGV encryption with numbers? like where m=8 (ring dimension), q=ciphertext modulus = 33=3*11 with level=2 What are COEFFICIENT and EVALUATION representation ?
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0answers
42 views

Can someone explain Relinearisation process in FV scheme for Homomorphic Encryption?

I am trying to understand the relinearisation process in FV scheme for Homomorphic Encryption based on R-LWE. Can one someone explain how the homomorphism keys are generated? I have worked out an ...
1
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0answers
81 views

How to solve a simple case of a RLWE problem

I've been reading up on the Ring Learning with Errors problem and the proposed attacks, in relation to homomorphic encryption. Some of the literature has been quite difficult to understand - what I ...
4
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1answer
178 views

Complete Attack on RLWE Key Exchange with reused keys, without signal leakage

I am studying a research paper "Complete Attack on RLWE Key Exchange with reused keys, without signal leakage" . On page number 21 to 28, there is toy example explaining the scheme. I am unable to ...
1
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0answers
57 views

How does the polynomial module impact the security of ring/lattices-based SIS problem?

Consider the following SIS problem: for a function $f_A(s)$=$As$, where $A$ is a fixed, randomly-chosen matrix in $(R_q)^{r \times n}$=$\left(\mathbb{Z}_q[X]/(X^N+1)\right)^{r \times n}$ and $q$ a ...
2
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0answers
104 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)...
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0answers
66 views

Discrete Gaussian Sampling in Authenticated key exchange from ideal lattices

I am implementing the key exchange scheme proposed by zhang et al. on Sage. In the implementation of the scheme, they have used the two distributions $\chi_{\alpha}, \chi_{\beta}$. How to choose $\...
1
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1answer
187 views

$\ell_2$-norm vs canonical embedding norm on ring-lwe

Ring-LWE based encryption (I pick up homomorphic encryption here) requires canonical embedding norm rather than $\ell_2$ norm to quantify the polynomial size (e.g. noise). Why is this better than $\...
28
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2answers
817 views

Uniform vs discrete Gaussian sampling in Ring learning with errors

The Wikipedia article on RLWE mentions two methods of sampling "small" polynomials namely uniform sampling and discrete Gaussian sampling. Uniform sampling is clearly the simplest, involving simply ...