Questions tagged [lattice-crypto]

Lattice-cryptography is the study and use of lattice problems applied to cryptography.

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Trapdoor for SIS

I am new to lattice cryptography. May I ask why, if one has a trapdoor for SIS, i.e., can compute a short $x$ that satisfies $Ax=0$, then one can have a trapdoor for $Ax_{2}=y$? TIA
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Difference between TFHE and CKKS?

What are the differences in parameters while implementing CKKS vs TFHE? For example modulus size, ring dimensions, bit security. Any pointers to literature would be appreciated
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Is there any bound on the size of ring dimension for Torus FHE?

I see that all implementations of TFHE in opensource supports 2^10 to 2^12 size of ring dimensions. Is there any specific reason (crypto) behind choosing the value or can we choose higher dimensions (...
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Reject sampling of lattice ZKP, why need factor of M

I am watching the video https://www.youtube.com/live/N5nKGtugxYY?si=ejLqW8Pk0jD9lVMn&t=2098 Or particularly this slide: May I ask why does the reject sampling output by $f(x)/g(x)*M$ probability? ...
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Decryption of LWE-based Inner-Product Fuctional Encryption of Agrawal-Libert-Stehle Crypto 2016

In below image, we have LWE-based inner-product functional encryption for short integers [ALS'Crypto2016]. Is the encryption correct? Why do they get $\mu\in\{\color{red}{-K+1},\ldots,0,K+1\}$? When ...
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lattice RLWE encryption and decryption process

I am here trying to solve an issue that I face a lot during solving RLWE. The issue is that I am not able to retrieve the original message after the decryption process. I use the following encryption ...
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1 vote
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ECDSA biased nonce with biased middle bits

The paper "Biased nonce sense" (https://eprint.iacr.org/2019/023.pdf) covers key recovery for MSB and LSB, the latter case being handled by doing modular inverse of 2 to the power of the ...
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Question of section 1.3 Intuition for Aborting in "Fiat-Shamir With Aborts: Applications to Lattice and Factoring-Based Signatures"

When I'm reading this paper "Fiat-Shamir With Aborts: Applications to Lattice and Factoring-Based Signatures" by Lyubashevsky. I have trouble understanding section 1.3 Intuition for Aborting....
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The general construction of a LWE-based PKE looks like the following: KeyGen : Secret vector, sk :$s \leftarrow \chi_s^m$ Public Key, pk: ($A \leftarrow \mathbb{Z}_q^{m \times m}, t = As + e)$ where $... • 95 3 votes 1 answer 32 views How to determine approximate factor (i.e. modulus-to-(bound of)noise ratio) of LWE in advaned primitives is sub-exponential or polynomial? In advanced primitives like circuit (policy) ABE [BGG+'Eurocrypt2014] or IPFE [ACGU'Asiacrypt2020, appedix A] based on lattices, parameters setting is quite puzzling and vague (for me). (Parameter ... • 490 1 vote 1 answer 54 views Literature on Batching in FHE From what I understand, the folklore way to batch Ring-LWE style cipher texts is to use the Chinese remainder theorem. I am wondering if there are any different approaches/optimizations to this style ... • 27 2 votes 0 answers 108 views Can this problem reduce to the SIS problem or LWE problem? The description of the graceless problem is as below. Given a full rank square matrix$A=(R\cdot S+E)\in\mathbb{Z}_q^{n\times n}$,where:$q>2^\lambda$is a prime;$R\leftarrow\mathbb{Z}_q^{n\times ...
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What would be the analogue of the gadget matrix in the ring setting? Would it be the same matrix? Do the trapdoor algorithms work exactly the same way? Thanks
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The definition of $\mathrm{SIS}_{q,n,m,\beta}$ problem is as below. Let $A\in\mathbb{Z}_q^{n\times m}$ be an $n\times m$ matrix with entries in $\mathbb{Z}_q$ that consists of $m$ uniformly random ...
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Shortest Vector Problem as Dihedral Hidden Subgroup Problem

I’m a mathematician trying to get into cryptography. I have a somewhat silly question, but I can’t seem to find a proper answer anywhere. I am interested in whether or not there is a way to directly ...
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Math of Hint usage in Dilithium

For Dilithium, I understand that $$\text{HighBits}(\mathbf{Ay}) = \text{HighBits}(\mathbf{Ay} - c\mathbf{s_2}) = \text{HighBits}(A_z - c\mathbf{t})$$ The first term of the equation is performed on the ...
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Is NTRU broken?

Today a new paper appeared on ePrint, "Improved Provable Reduction of NTRU and Hypercubic Lattices". It claims that: this is the first provable result showing that breaking NTRU lattices ...
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CRYSTALS-Kyber Compress and Decompress function role

I was reading CRYSTALS-Kyber design. They have used compress_q(x,d) to scale an element of $\mathbb{Z}_q$ to $[ 0,1,...,2^d-1 ]$. The definitions of ...
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Do you know any library for implementing lattice-based schemes? [closed]

Good afternoon! I'm trying to write a code for a lattice based scheme (based on the SIS problem). I'm looking for a library that may help me in this task without taking care of the implementation of ...
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Decision LWE vs Search LWE: Which one is harder?

Sometimes if we have an attacker who's able to solve decision-LWE problem then we can use them (as a sub-routine) to solve (search) LWE problem, i.e., $\mathsf{sLWE} \leq \mathsf{dLWE}$. Conversely, ...
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Understanding Gentry's initial FHE construction based on ideal lattices

I am trying to understand the encryption procedure in Craig Gentry's initial construction for FHE described in Fully Homomorphic Encryption Using Ideal Lattices. Unfortunately after repeated attempts ...
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