elliptic curves - 2024 PLAYTIME

Question

The Weil pairing matches the n-torsion points on these structures to the nth roots of unity. For 10 points each:

[10h] Identify these structures used by Lenstra factorization to achieve subexponential runtime. Isogenies between these structures formed the basis of the now-deprecated SIKE protocol.

ANSWER: elliptic curves [or ECs]

[10e] In 2007, Shumow and Ferguson constructed a theoretical attack on Dual_EC, an elliptic curve algorithm that generated deterministic bits with this property. Numbers with this property may be generated by rolling a die.

ANSWER: random [accept pseudorandom]

[10m] Dual_EC was a cryptographic standard published by this organization in a NIST publication. This organization developed the AES algorithm as well as the SHA family of hash functions.

ANSWER: the NSA [or National Security Agency]

<CT, Other Science - Computer Science>

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Summary


2025 PLAYTIME @ CWRU	12/10/2024	Y	5	14.00	80%	60%	0%
2025 PLAYTIME @ Claremont	12/10/2024	Y	5	16.00	100%	40%	20%
2025 PLAYTIME @ Florida	12/10/2024	Y	2	10.00	100%	0%	0%
2025 PLAYTIME @ Florida	12/10/2024	Y	1	20.00	100%	100%	0%
2024 PLAYTIME @ Harvard	04/26/2025	Y	4	17.50	100%	50%	25%
2024 PLAYTIME @ JHU	10/26/2024	Y	8	15.00	100%	38%	13%
2025 PLAYTIME @ Northwest	12/10/2024	Y	4	15.00	100%	25%	25%
2025 PLAYTIME Online	04/26/2025	Y	9	17.78	100%	33%	44%
2025 PLAYTIME @ Sheffield	12/10/2024	Y	6	10.00	100%	0%	0%
2025 PLAYTIME @ Sheffield	12/10/2024	Y	1	20.00	100%	100%	0%
2024 PLAYTIME @ UBC	10/05/2024	Y	8	11.25	100%	13%	0%
2024 PLAYTIME @ Virginia Tech	07/11/2025	Y	3	20.00	100%	67%	33%
2024 PLAYTIME @ WashU	10/12/2024	Y	6	10.00	83%	17%	0%

Data


Ohio State D	Michigan C	0	10	0	10
Michigan A	Ohio State A	0	10	10	20
Michigan B	Oberlin	0	10	10	20
Michigan D	Ohio State B	0	0	10	10
Pittsburgh	Ohio State C	0	10	0	10
Art of Premature Signaling	UCLA A	10	10	10	30
girl 15 whale i mean they	Caltech	0	10	0	10
Claremont A	UCSB	0	10	0	10
Claremont B	UCLA B	0	10	0	10
Billy's Bastion	Edwin Laundrorat's Long-Lost Man Unclothès Rat Degrosses	0	10	0	10
Too much from you lately	Keeping Up With the Cardassians	0	10	0	10
Project2025BC: Make Assyria Great Again	Qin Shi Huang's Immortality Poison	0	10	10	20
UCSD	P.C.‚ Daniel‚ Michel‚ and Jason B	0	10	10	20
Brandeis	Belmont	0	10	10	20
BU	Brown	0	10	0	10
RIT	Harvard	10	10	10	30
MIT	Lexington	0	10	0	10
NYU B	Catholic University of America	0	10	10	20
Haverford B	George Mason B	10	10	10	30
Georgetown	George Washington	0	10	10	20
George Mason A	Haverford A	0	10	0	10
Johns Hopkins A	Rutgers	0	10	0	10
Maryland A	Johns Hopkins B	0	10	0	10
NYU A	George Mason C	0	10	0	10
CWRU	NYU C	0	10	0	10
Carleton	Alberta	0	10	0	10
Arizona State University A	Arizona State University B	10	10	10	30
UW A	South Dakota School of Mines	0	10	0	10
Washington Connections	UW B	0	10	0	10
Egypt Airlines Haters	Quatumvirate	10	10	0	20
Four Generalists in Search of a Power	we need new names	0	10	0	10
Mahjonng Masters	Goober Gang	0	10	0	10
Gruh	Notre Dame + Epic Games	0	10	0	10
Monsieur Hulot's Academic Team	Illinois Orange	10	10	10	30
Free Agents 1	MSJ	10	10	10	30
Mike Dukakis Tank Battalion	Auburn 2026	10	10	0	20
Trip-Hop Quizzer Tricky	2 Italians, 2 Poles, All Noles	0	10	10	20
evil women enjoyers	mongeese	0	10	0	10
Cambridge	Edinburgh	0	10	10	20
Manchester	Imperial B	0	10	0	10
Lancaster	Sheffield B	0	10	0	10
Sheffield C	Sheffield A	0	10	0	10
Imperial A	Warwick A	0	10	0	10
Warwick B	LSE	0	10	0	10
Birmingham	Warwick C	0	10	0	10
Simon Fraser	McGill A	0	10	0	10
Ottawa A	Mac A	0	10	0	10
Toronto A	Toronto Metropolitan	0	10	0	10
Toronto B	Waterloo B	0	10	0	10
Waterloo A	Toronto C	0	10	0	10
Guelph	Toronto E	0	10	0	10
UBC	McGill B	0	10	10	20
Waterloo C	Toronto D	0	10	0	10
4 quizbowl pros go Virginia on North Carolina	Ashurbanipal’s Drag Race	10	10	10	30
Adrianne Lenker 4 Nobel Lit Prize 2K65	Even in Blacksburg There I Am	0	10	10	20
Master and Margaritaville	Somehow Paula Deen Returned	0	10	0	10
WashU Bulbasaur	Iowa State	0	0	0	0
Illinois C	Chicago A	0	10	0	10
WashU Charmander	Illinois A	0	10	0	10
Illinois B	Chicago B	0	10	0	10
SIUE	Missouri	0	10	0	10
Truman State	WashU Squirtle	0	10	10	20