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]
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