Questions tagged [ideal-lattices]
5 questions
4
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1 answer
Can be the matrix A in the LWE assumption a square matrix?
In the LWE assumption, if I set $m=n$, making $A$ an $n\times n$ square matrix, provided that $\det(A)\neq0(\mod q)$(i.e., full rank), is the LWE assumption still valid?
In this case, $A$ is invertible $\mod q$, one may recover the secret via…
X.H. Yue
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2
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1 answer
Basis of Cyclic Lattices
I am studying The Mathematics of Lattice-Based Cryptography from Alfred Menezes' Cryptography 101 course. In slide 6 (Ring-SIS and Ring-LWE), page 83, it states that $L(A)$ is a rank $n$ lattice. I understand that a lattice's rank cannot exceed its…
Omid Bodaghi
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2
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1 answer
Modulus in Lattice-Based Cryptography？
The common modulus methods are standard modulus (the result is confined to the range $[0, q-1]$) and centered modulus (the result is confined to the range $[- \lfloor q/2 \rfloor, \lceil q/2 \rceil)$).
My questions is：In lattice-based cryptography,…
user109993
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2
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1 answer
Understanding Canonical-embedding vs Coefficient-embedding in Ideal Lattices: Relation to NTT?
I'm trying to understand the relationship between different representations of ideal lattices, particularly the canonical embedding and coefficient embedding. While studying these concepts, I noticed some similarities between:
Canonical embedding…
a15600712
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0
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Why consider/formulate Shortest Vector Problem as a Promise Problem and not as a Decision Problem?
We know (search) approximate Shortest Vector Problem ($\mathsf{SVP}_{\gamma}$): Given an arbitrary basis $\mathbf{B}$ of some lattice $\mathcal{L}=\mathcal{L}(\mathbf{B})$, find a shortest non-zero lattice vector, i.e., a $\mathbf{v}\in\mathcal{L}$…
user1035648
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