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LWE instances have the form $\vec{a}_i,b_i = <\vec{a}_i,\vec{s}>+e_i~mod~q$ for some integer $q$ and for $i=1,\dots,m$.

My questions are about the NIST proposed standards. In the standards

1. Do we allow $q=2^t$ (if not why not?)? and what is relation between $q$ and $n$ where $n$ is length of $\vec{a}_i$?

2. How large can $m$ be?

LWE instances have the form $\vec{a}_i,b_i = \langle\vec{a}_i,\vec{s}\rangle+e_i\bmod q$ for some integer $q$ and for $i=1,\dots,m$.

My questions are about the NIST proposed standards. In the standards

1. Do we allow $q=2^t$ (if not why not?)? and what is relation between $q$ and $n$ where $n$ is length of $\vec{a}_i$?

2. How large can $m$ be?

LWE instances have the form $\vec{a}_i,b_i = <\vec{a}_i,\vec{s}>+e_i~mod~q$ for some integer $q$ and for $i=1,\dots,m$.

My questions are about the NIST proposed standards. In the standards

1. Do we allow $q=2^t$? and what is relation between $q$ and $n$ where $n$ is length of $\vec{a}_i$?

2. How large can $m$ be?

LWE instances have the form $\vec{a}_i,b_i = <\vec{a}_i,\vec{s}>+e_i~mod~q$ for some integer $q$ and for $i=1,\dots,m$.

My questions are about the NIST proposed standards. In the standards

1. Do we allow $q=2^t$ (if not why not?)? and what is relation between $q$ and $n$ where $n$ is length of $\vec{a}_i$?

2. How large can $m$ be?

LWE instances have the form $\vec{a}_i,b_i = <\vec{a}_i,\vec{s}>+e_i~mod~q$ for some integer $q$ and for $i=1,\dots,m$.

My questions are about the NIST proposed standards. In the standards

1. Do we allow $q=2^t$ or $q=2^tl$ where $l$ is odd?

2. How large can $m$ be?

LWE instances have the form $\vec{a}_i,b_i = <\vec{a}_i,\vec{s}>+e_i~mod~q$ for some integer $q$ and for $i=1,\dots,m$.

My questions are about the NIST proposed standards. In the standards

1. Do we allow $q=2^t$? and what is relation between $q$ and $n$ where $n$ is length of $\vec{a}_i$?

2. How large can $m$ be?