A new paper by Fluhrer is relevant to the discussion about scalar blinding with special-prime vs random-prime curves:
http://eprint.iacr.org/2015/801 My earlier impression [1] was that scalar-blinding on 25519 might use a 128-bit blinding factor, whereas a similar-but-random-prime curve would use a 64-bit blinding factor, resulting in a slowdown for 25519 of around (256+128)/(256+64) = 1.2. Fluhrer's paper argues for using the same size blinding factor, but recoding the digits of the scalar used for windowing into a form where the group's order "would, at first glance, appear random". He gives an example of base-48 digits instead of base-32, and estimates a slowdown for 25519 of around 1.1. I don't think this helps implementations that use Montgomery ladder (instead of windowing). Beyond that, I don't have a good sense how well this would work, how awkward the encoding would be, or how it would interact with other scalar encoding methods. Anyone have a more informed opinion? Trevor [1] https://moderncrypto.org/mail-archive/curves/2015/000563.html _______________________________________________ Curves mailing list [email protected] https://moderncrypto.org/mailman/listinfo/curves
