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U-Prove Recommended Parameters describes the groups used by U-Prove. For the subgroup variant it references Appendix A.1.1.3 of FIPS186-3 which is about groups for finite-field based DSA. AFAIK these groups are Schnorr groups, even though NIST never refers to them as such. The ECC variant uses standard NIST curves such as P-256, P-384 and P-521.


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The usual way to encode long random bitstrings, so that they can be easily memorized and/or entered by humans, is to break them into blocks of (typically) 10 to 12 bits and map each block to an entry in a fixed dictionary of common words. This approach is commonly used for secure passphrase generation, e.g. by Diceware, S/KEY and PGP. Assuming an 11-bit ...


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If what you want is some kind of algorithm that takes a public key $Q = aP$ on one curve and converts it into $Q' = a P'$ on the other curve, then the answer is almost certainly no. There are no "interesting" maps between curves with different group structures. If you just want to use the same secret key for both curves, so $Q = aP$ on one curve and $Q' = ...


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My goal is to create a voting scheme that doesn't require a lot of crypto infrastructure ... I would like these anonymised ballots to be publicly accessible for verification. It sounds to me like you want a end-to-end voter verifiable voting system. Some of them do require a lot of crypto infrastructure, but it sounds like several others already ...



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