Academic Bibliography
https://biblio.ugent.be/
Ghent University Academic Bibliography2000-01-01T00:00+00:001monthlyCSIDH on the surface
https://biblio.ugent.be/publication/8665496
Ding, J.Tillich, J. P.Castryck, WouterDecru, Thomas2020For primes p≡3mod4, we show that setting up CSIDH on the surface, i.e., using supersingular elliptic curves with endomorphism ring Z[(1+−p−−−√)/2], amounts to just a few sign switches in the underlying arithmetic. If p≡7mod8 then horizontal 2-isogenies can be used to help compute the class group action. The formulas we derive for these 2-isogenies are very efficient (they basically amount to a single exponentiation in Fp) and allow for a noticeable speed-up, e.g., our resulting CSURF-512 protocol runs about 5.68% faster than CSIDH-512. This improvement is completely orthogonal to all previous speed-ups, constant-time measures and construction of cryptographic primitives that have appeared in the literature so far. At the same time, moving to the surface gets rid of the redundant factor Z3 of the acting ideal-class group, which is present in the case of CSIDH and offers no extra security.application/pdfhttps://biblio.ugent.be/publication/8665496http://hdl.handle.net/1854/LU-8665496http://dx.doi.org/10.1007/978-3-030-44223-1_7https://biblio.ugent.be/publication/8665496/file/8665498engSpringerI have transferred the copyright for this publication to the publisherinfo:eu-repo/semantics/openAccessPost-quantum cryptography, 11th international conference, PQCrypto 2020ISSN: 0302-9743ISSN: 1611-3349ISBN: 9783030442224ISBN: 9783030442231Mathematics and StatisticsIsogeny-based cryptographyHard homogeneous spacesCSIDHMontgomery curvesCSIDH on the surfaceconferenceinfo:eu-repo/semantics/conferenceObjectinfo:eu-repo/semantics/publishedVersionTranslating between the roots of the identity in quantum computers
https://biblio.ugent.be/publication/8564845
Castryck, WouterDemeyer, JeroenDe Vos, AlexisKeszocze, OliverSoeken, Mathias2018The Clifford+T quantum computing gate library for single qubit gates can create all unitary matrices that are generated by the group < H, T >. The matrix T can be considered the fourth root of Pauli Z, since T-4 = Z or also the eighth root of the identity I. The Hadamard matrix H can be used to translate between the Pauli matrices, since (HTH)(4) gives Pauli X. We are generalizing both these roots of the Pauli matrices (or roots of the identity) and translation matrices to investigate the groups they generate: the so-called Pauli root groups. In this work we introduce a formalization of such groups, study finiteness and infiniteness properties, and precisely determine equality and subgroup relations.application/pdfhttps://biblio.ugent.be/publication/8564845http://hdl.handle.net/1854/LU-8564845http://dx.doi.org/10.1109/ISMVL.2018.00051https://biblio.ugent.be/publication/8564845/file/8564849engIEEEI have transferred the copyright for this publication to the publisherinfo:eu-repo/semantics/restrictedAccess2018 IEEE 48th international symposium on multiple-valued logic (ISMVL 2018)ISSN: 0195-623XISSN: 2378-2226ISBN: 9781538644645ISBN: 9781538644638Mathematics and Statisticsquantum computermatrix groupTranslating between the roots of the identity in quantum computersconferenceinfo:eu-repo/semantics/conferenceObjectinfo:eu-repo/semantics/publishedVersion