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Concrete quantum cryptanalysis of binary elliptic curves

Gustavo Banegas, Daniel J. Bernstein, Iggy Van Hoof, Tanja Lange
2020 Transactions on Cryptographic Hardware and Embedded Systems  
For field multiplications, we benefit from the recent space-efficient reversible Karatsuba algorithm from Van Hoof [Hoo20] for multiplying polynomials.  ...  Multiplication For multiplication we use a space-efficient Karatsuba algorithm by Van Hoof [Hoo20] which uses O(n 2 ) CNOT gates, O(n log 2 3 ) Toffoli gates and 3n total qubits: 2n qubits for the input  ... 
doi:10.46586/tches.v2021.i1.451-472 fatcat:2chsn37mzba27ktdutfaq7oc2q

Space-efficient quantum multiplication of polynomials for binary finite fields with sub-quadratic Toffoli gate count [article]

Iggy van Hoof
2020 arXiv   pre-print
Multiplication is an essential step in a lot of calculations. In this paper we look at multiplication of 2 binary polynomials of degree at most n-1, modulo an irreducible polynomial of degree n with 2n input and n output qubits, without ancillary qubits, assuming no errors. With straightforward schoolbook methods this would result in a quadratic number of Toffoli gates and a linear number of CNOT gates. This paper introduces a new algorithm that uses the same space, but by utilizing
more » ... ent variants of Karatsuba multiplication methods it requires only O(n^log_2(3)) Toffoli gates at the cost of a higher CNOT gate count: theoretically up to O(n^2) but in examples the CNOT gate count looks a lot better.
arXiv:1910.02849v2 fatcat:ti2pxvhncrebze4zde6hrj6dd4

Page 72 of Albion, a Journal of News, Politics, and Literature Vol. 41, Issue 6 [page]

1863 Albion, a Journal of News, Politics, and Literature  
says iggy, as he turned and looked up at the black sky to windward; but Toby did not offer to move.  ...  The =A was slipping and tumbling about the decks, for the ship lay over so much with the breeze, being close hauled, that he could not keep his hoofs.  ... 

The Dutch Society of Nephrology

1986 Kidney International  
LEUNISSEN KML, VANLEENDERTR, VISMANS F, and VAN HOOF JP. Department of Internal Medicine, St. Annadal Hospital, 6201 BX, Maastricht, The Netherlands.  ...  MULLER EW, VAN DER WOUDE FJ, GROND AJK, DONKER AJM, and VAN DER HEM GK.  ... 
doi:10.1038/ki.1986.89 fatcat:6h6tghtyuzdpragdvaduusw6f4

Page 125 of Spirit of the Times Vol. 7, Issue 16 [page]

1837 Spirit of the Times  
Ti iggis y Star, da s, by G custom: e weigh ehall rderous p to ne 1 them, keepi y runai lack ne all.  ...  Gips ™ » MS fr about 3:47 isian of hoof: k this - stands desi | HURS ime r acket , dam ares u e.— itable ipsey wa riends “47, sce.  ... 


J Meijers
Hy is 'n boom wat diep en vas geplant, Sy wortels uitsprei by die waterkant; En mild versorg deur vrugb're lentelugte, Sy volle drag laat sien van somervrugte.  ...  HOOFDSTUK X ENKELE AFWIJKENDE TAAL VORMEN We laten in deze laatste les nog enkele vormen de revue passeren, waarin het Afrikaans sterk van het Nederlands afwijkt.  ...  Afr. hoof wordt alleen figuurlijk gebruikt: die man is hoof van die gesin. Afr. reg = juist, in orde. Jy het reg = jij hebt gelijk. Alles sal regkom as alkeen sy plig doen.  ... 


Onderworpenheid Eintlike, Strydpunt
'n parodic b evat op die , nuwe Britse vrybeid" waarvolgens Jede van die Ryk toegelaat word om , vrye Republiek e" te word terwyl bulle nog binne die Empire bly.  ...  In die artikel is die nuwe vr ybeid gebek el deur dit te vergelyk m et handiete lndiers Leer Van Britse Diplomasie DU ITSE VERSET wat nou , vry" word dcur ' n , bandietehond" binne die tronk te stig.  ...  J. du Plessis, hoof van die afdeling plantsiektelecr aan die Landboukollege Stellenboseb-Elsenburg, sal vanjaar die Havenga-prys vir wetenskaplike navorslng van die Akademie vir Kuna en Wetenskap ontvang  ... 

Improved quantum circuits for elliptic curve discrete logarithms [article]

Thomas Häner and Samuel Jaques and Michael Naehrig and Martin Roetteler and Mathias Soeken
2020 arXiv   pre-print
We thank Dan Bernstein, Martin Ekerå, Iggy van Hoof, and Tanja Lange for helpful suggestions about elliptic curve arithmetic.  ... 
arXiv:2001.09580v1 fatcat:6yd2bpqxb5gfncae3qmh2bs4uu

The inhibitory activity of secretions in cattle against foot and mouth disease virus

A. J. M Garland
Al19 and A4691 (Van Bekkum et al 1959 , Burrows 1966~ Sutmoller and McVicar 1972 .  ...  In the original observations of Van £ekkum et al (1959) (Hedger and Stubbins.197l ).  ... 
doi:10.17037/pubs.00878722 fatcat:hs5beugib5fzhaiioicwduyguy

Meanings in motorcycling

Robert Gordon Reeves
She's talking to him, just getting over her nervousness, when Iggy slams her on both shoulders.  ...  Iggy, also known as Pig Pen, is hustling a fairly straight looking girl late one July night in Memorial Park.  ... 
doi:10.14288/1.0302436 fatcat:xlbyjremlrdmpcnwa23vxcfcm4

Sea of Dreams: André Breton and the Great Barrier Reef

Ann Elias
By the mid-70s, Oursler tells us, Mike was emerging from the spell of the Detroit scene: the Hairy Who, Blue Cheer, Iggy Pop, R.  ...  Wooton Vanbrugh; wheels of circling flowers and animals permeate the whole night sky: The primal beast alone filled the entire empyrean, one figure, one essential animal … winged, four legged, horned, hoofed  ... 

The Daily Texan [article]

University Of Texas At Austin, Austin, The University Of Texas At
iggiing rn c e 1 an offense e sp ark going for the Oilers. "T would think, though, lf we d id som ething like thai-, w ed want to talk to him first."  ...  V A N H E U S E N Van Heusen turns nuclear fission into nuclear fashion and crea te s an ener getic new collection of 417 dress and sport shirts!  ... 
doi:10.26153/tsw/31406 fatcat:utvzc3mf6veedd4skgqxtgjtne

A Collection of Borrowed Exaggerations [article]

Douglas Neilson, University Of Calgary, University Of Calgary, Aritha Van Herk
There's a mini-van parked in the lot, and the back window has all those family stickers that middle-aged van-types slap on their vans in place of having any sort of self-respect.  ...  Iggy. Cammy. The puck eventually gets to a defender in the far corner who pounds it up the boards toward a streaking forward.  ... 
doi:10.11575/prism/24662 fatcat:25y2djmqvnejvarvt6aknzxtnu

The mechanisms of antibody generation in the llama

Ben Woolven
The order Artiodactyl includes hoofed mammals such as the pig, giraffe and hippopotamus (none of which are known to express heavy chain antibodies).  ...  Antibody/antigen association is typically the combined result of non-covalent electrostatic, van der Waals and hydrogen bond interactions.  ... 
doi:10.22024/unikent/01.02.86217 fatcat:p7kfsna7gvac5lbqkenq4nz7ci