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Three's Compromised Too: Circular Insecurity for Any Cycle Length from (Ring-)LWE [chapter]

Navid Alamati, Chris Peikert
<span title="">2016</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
In this work we construct k-circular security counterexamples for any k ≥ 2 based on (ring-)LWE.  ...  Moreover, both schemes are k -circular insecure for 2 ≤ k ≤ k. Notably, our ring-LWE construction does not immediately translate to an LWE-based one, because matrix multiplication is not commutative.  ...  Contributions Our main contributions are k-circular security counterexamples, for any k ≥ 2, based on the LWE [Reg05] and ring-LWE [LPR10] assumptions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.1007/978-3-662-53008-5_23</a> <a target="_blank" rel="external noopener" href="">fatcat:xlv7wvkb6nfttefkbqcjbmufry</a> </span>
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