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5
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115 views

Given a 'good' basis for a lattice, how can we solve the CVP?

I'm doing a little bit of reading about lattices. I read that if we can find a 'short' basis for our given lattice, we can solve CVP and SVP very efficiently. However, the paper didn't describe an ...
3
votes
0answers
51 views

How to generate new LWE samples

Assume we are given a small fixed number of LWE samples with secret $s$ and error $e$, where the error distribution is taken so that the LWE problem is hard. My question: How can one further ...
3
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0answers
67 views

How to recover $e$ from $f_A(e) = Ae \mod q$ when knowing trapdoor

I have a silly question, but I don't know a solution, so I need to question. Assume, with a algorithm $TrapGen(1^\lambda)$, it generates $A\in\mathbb{Z}_q^{n\times m}$ with a basis $B ...
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0answers
31 views

How can a lattice attack be applied to ECDSA signatures?

The aim is to check if it is possible to break the ECDSA cryptosystem under the following criteria. Suppose that each ECDSA signature is generated by using the GLV method for point multiplication ...
0
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0answers
104 views

The Inhomogeneous Short Integer Solution (ISIS) problem with a clue

The Inhomogeneous Short Integer Solution (ISIS) problem is as follows: given an integer $q$, a matrix $A \in \mathbb Z^{n\times m}_q$, a vector $b\in \mathbb Z^n_q$, and a real $\beta$, find an ...
0
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128 views

The Short Integer Solution (SIS) problem for square matrices

The short (or small) integer solution (SIS) problem is as follows: given an integer $q$, a matrix $A \in \mathbb Z^{n\times m}_q$, and a real $\beta$, find a nonzero integer vector $e\in \mathbb Z^m$ ...