English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The Isogeny to Endomorphism Ring Problem (IsERP) asks to compute theendomorphism ring of the codomain of an isogeny between supersingular curves incharacteristic $p$ given only a representation for this isogeny, i.e. some dataand an algorithm to evaluate this isogeny on any torsion point. This problemplays a central role in isogeny-based cryptography; it underlies the securityof pSIDH protocol (ASIACRYPT 2022) and it is at the heart of the recent attacksthat broke the SIDH key exchange. Prior to this work, no efficient algorithmwas known to solve IsERP for a generic isogeny degree, the hardest caseseemingly when the degree is prime.  In this paper, we introduce a new quantum polynomial-time algorithm to solveIsERP for isogenies whose degrees are odd and have $O(\log\log p)$ many primefactors. As main technical tools, our algorithm uses a quantum algorithm forcomputing hidden Borel subgroups, a group action on supersingular isogeniesfrom EUROCRYPT 2021, various algorithms for the Deuring correspondence and anew algorithm to lift arbitrary quaternion order elements modulo an odd integer$N$ with $O(\log\log p)$ many prime factors to powersmooth elements.  As a main consequence for cryptography, we obtain a quantum polynomial-timekey recovery attack on pSIDH. The technical tools we use may also be ofindependent interest.

Hidden Stabilizers, the Isogeny To Endomorphism Ring Problem and the Cryptanalysis of pSIDH