We show how any pair of authenticated users can on-the-fly agree on an el- liptic curve group that is unique to their communication session, unpredictable to outside observers, and secure against known attacks. Our proposal is suitable for deployment on constrained devices such as smartphones, allowing them to efficiently generate ephemeral parameters that are unique to any single cryptographic application such as symmetric key agreement. For such applications it thus offers an alternative to long term usage of stan- dardized or otherwise pre-generated elliptic curve parameters, obtaining security against cryptographic attacks aimed at other users, and eliminating the need to trust elliptic curves generated by third parties.
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