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Re:What We Do in the /etc./Shadow – Cryptography with Passwords by Oreko on Saturday January 07, 2023 @06:12PM (#34294044)
Augmented is a common label for these kind of PAKEs. Generally speaking, asymmetric, verifier-based, and augmented are all three interchangeable.

Sc00bz made this comment[1] on reddit describing what "doubly augmented" means where they succinctly describe it as

"A doubly augmented PAKE is where both sides can store data to authenticate with eachother but not themselves."

This mirrors the definition of aPAKE and makes sense, but this sounds more like the security property provided by CRISP[2]. This doesn't make sense in the context of double BS-SPEKE as the client inputs their password in the clear which can be used to generate the server's storage without any "guessing".

[1] https://old.reddit.com/r/crypto/comments/zy8w3y/what_we_do_i...

[2] CHIP and CRISP: Protecting All Parties Against Compromise through Identity-Binding PAKEs https://eprint.iacr.org/2020/529

Re:What We Do in the /etc./Shadow – Cryptography with Passwords by cendyne on Saturday January 07, 2023 @08:41PM (#34295119)
Thank you for these resources!
Re:What We Do in the /etc./Shadow – Cryptography with Passwords by Oreko on Saturday January 07, 2023 @10:25PM (#34295703)
Another confusion on my part, above the protocol Sc00bz writes:

" Client without password has:

      idC = client identity

      P = hashToPoint(p)

      c

      S = s * P

      Reg = reg * G (reg = registration private key)
"