# Questions tagged [lwe]

Learning with Errors is a form of lattice problem used in the design of cryptographic primitives. LWE is based on the Closest Vector Problem (CVP).

44 questions
63 views

102 views

76 views

### Why don't we use an Extendable Output Function to efficiently store the public key of Regev's LWE-based encryption scheme over standard lattices?

In LWE-based schemes the public key is generated by choosing a random matrix (or polynomial) $A$, and outputting the pair $(A, b = A\cdot s + e)$, where $s$ and $e$ are vectors/polynomials with ...
81 views

### Distinguishing advantage in terms of $\Omega(\omega)$

I was going through this paper ("Fully Homomophic Encryption over the Integers Revisited") and the statement written in the first paragraph on page 5 stating $\DeclareMathOperator{\agcd}{AGCD}$ We ...
183 views

### ring-LWE: Minkowski Embedding , the Co-Different Ideal, etc

While (trying) to go over the reductions from approx. SVP on ideal lattices to search ring-LWE,  and , for $K = \mathbb{Q}(\zeta)$ where $\zeta$ is an abstract root of a cyclotomic polynomial, ...
60 views

53 views

### show how LWE errors can have a greater impact on result

Hi weve been given the following question in one of our classes but have not been taught anything about it and is worded strangely. It is to show how the LWE problem works by showing how small errors ...
33 views

168 views

### Pseudorandomness of ring learning with errors

My question is in Ring Learning with Errors, let $a(x)\in \mathbb{Z}_q(x)/(X^n+1)$ where $n$ is a power of $2$, be a random polynomial, $s(x),e(x)\in \mathbb{Z}_q(x)/(X^n+1)$ are the secret and error ...
201 views

### CCA2-secure encryption based on LWE/Ring-LWE

As I understand it, cryptosystems based on LWE/Ring-LWE are typically only IND-CPA, and fail to satisfy IND-CCA2. In fact, it appears that chosen ciphertext attacks could allow secret key recovery (!)...
155 views

### A Simple Provably Secure Key Exchange Scheme Based on the LWE

In this paper (A simple provably secure key exchange by Ding et al.), I am trying to understand the correctness (which is given on page number 8) of the key exchange technique based on LWE. To ...
147 views

### Security estimation of LWE using “On dual lattice attacks against small-secret LWE and parameter choices in HElib and SEAL”

I recently found this paper eprint which estimates security of LWE instantiations using an improved Dual attack. However, I got confused looking at their example in this site. For example, in the case ...
265 views

### How the condition $s \geq 8$ is determined in Lindner-Peikert cryptosystem?

In Lindner & Peikert paper, the authors propose that to set the cryptosystem's parameters, one should choose $q$ to be large enough to allow for a Gaussian parameter $s \geq 8$. My question is, ...
250 views

### A Simple Provably Secure Key Exchange Scheme Based on the Learning with Errors Problem

In this paper (A simple provably secure key exchange by Ding et al.) At page number 8, the author gives correctness of the technique as follows then SK A = SKB with overwhelming probability i.e. if ...
126 views

### How to provide security against malicious adversary in Ring LWE homomorphic encryption scheme?

I was reading Ring LWE homomorphic encryption scheme referred in http://www.wisdom.weizmann.ac.il/~zvikab/localpapers/IdealHom.pdf But this encryption scheme provides security mostly in the semi-...
631 views

### Why is Ring-LWE more efficient compared to LWE?

Can someone please tell me why is the Ring-LWE more efficient? By introducing polynomials in place of matrices, what kind of optimizations do we introduce that make Ring-LWE more efficient?
171 views

### LWE: error and float operations

Background I'm trying to make sense of the error in implementations of LWE and R-LWE. In LWE and R-LWE error is added to vectors in lattices to make it computationally infeasible to recover any ...
83 views

### LWE status versus modern deployed crypto [closed]

LWE is the one of the most promising post quantum strategy. How does parameters (key sizes, time for encryption etc) for LWE compare with modern deployed standards such as Factoring or discrete log ...
151 views

### Number of LWE samples in NewHope

This is regarding the number post-quantum key exchange protocol New-Hope (https://eprint.iacr.org/2015/1092.pdf). In the paper, we can see that the number of samples generated by the protocol is $2n$ ...
231 views

### Understand LWE(Learning With Error) negligible error probability

According to Regev's paper, p15 Correctness. Note that if not for the error in the LWE samples, $b-⟨a, s⟩$ would be either 0 or ⌊ q ⌋ depending on the encrypted bit, and decryption would always be ...
185 views

### Why in BCNS protocol both parties don't follow the exact same key extraction approach

Why in BCNC key-exchange protocol (page 8), Bob instead of: $K_B \leftarrow \lfloor \bar v \rceil_{2q,2} \in \{ 0, 1\}^n$ do this instead: $K_B \leftarrow rec(2bs', c) \in \{0, 1\}^n$. or they are ...
135 views

### Security of Lindner-Peikert parameters for lwe

From Regev's paper in 2005, we know that for applying worst-case to average-case reduction to an lwe cryptosystem, one should use error distributions with standard deviation $s$ bigger than $2\sqrt{n}$...