$$ \def\Fp{\mathbb{F}_p} \def\deq{\mathrel{\mathop:}=} \def\range#1{[{#1}]} \def\alg#1{\textsf{#1}} \def\rank{\textsf{rank}} \def\msb{\textsf{msb}} \def\bit{\textsf{bit}} \def\mib#1{\color{blue}{\mathbf{{#1}}}} \def\mir#1{\color{red}{\mathbf{{#1}}}}

$$ \def\Zq{\mathbb{Z}_q} \def\EE{\mathbb{E}} \def\deq{\mathrel{\mathop:}=} \def\range#1{[{#1}]} \def\PK{\textit{pk}} \def\SK{\textit{sk}} \def\ct{\textit{ct}} $$

$$ \def\Fp{\mathbb{F}_p} \def\FF{\Fp^{\scriptscriptstyle{(<n)}}[X]} \def\com{\mathbf{com}} \def\range#1{[{#1}]} $$ Dan Boneh, Ben Fisch, Ariel Gabizon, and Zac Williamson Let's construct a simple zero knowledge range proof from a