[Hard] Rewrite cryptographic verification for CIBA (Client Initiated Backchannel Auth)

[keepsloading]

Implementation issue mapping to the CIBA (Client Initiated Backchannel Auth) epic for the Notebook repository.

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Friendly reminder for SSoC26 contributors: When you submit a Pull Request for this issue, please remember to also raise a dummy PR in the Memact/Context repository that references your original PR. This is required for your contribution to be considered for points on the SSoC leaderboard!

[Akshatshukla-25]

assign me