Cryptography in Distributed Systems

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" summary

Claims a secret-shared q-SDH accumulator with constant-size witnesses that uses MPC (SPDZ or Shamir) so all updates and witness creation run in constant time while initial accumulation stays O(n) and works in practice via MP-SPDZ+Relic. Benchmarks show non-MPC updates cost >100s for 2^14 items but the SPDZ instantiation runs under 0.25s in LAN and under 4s in WAN. The identity scheme uses blind Pointcheval‑Sanders signatures, Dodis‑Yampolskiy PRF, threshold ElGamal/Shamir and NIZKs to enforce a MaxACC limit and recover PRF keys for revocation. A separate result gives non-interactive half-aggregation for Schnorr/EdDSA: a Sigma-based compressor that achieves ~50% size reduction, Fiat‑Shamir aggregates 1000 signatures in <1ms, Fischlin gives tighter security at higher cost.

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" chapters (26)

1. 0:00Intro
2. 2:02Accumulators in Digital Identity Management
3. 2:24Digital Identity Management - Authentication
4. 2:41Digital Identity Management - Anonymous Credentials
5. 3:12Digital Identity Management - Accumulator updates
6. 7:11MPC protocols and Implementation
7. 8:07Keyless q-SDH benchmark
8. 10:36Conclusion
9. 11:55Distributed payment systems
10. 15:02Registration
11. 16:16Account Creation in more detail
12. 18:01Anonymity Revocation
13. 19:10Accounts Tracing
14. 20:06Cryptographic Tools and Techniques
15. 21:19Security Analysis
16. 22:46Schnorr Signatures
17. 23:31Signature Aggregation
18. 24:29Application: Compressing Blockchains
19. 24:47Problem Scope
20. 26:25Quick recap: Sigma Protocol for relation R
21. 27:03Sigma Protocol for Pok of Schnorr Signature
22. 28:21Compressing Poks for n discrete logarithm instances
23. 29:29Compressed Sigma Protocol for Pok of n Schnorr Sigs
24. 31:00From Sigma Protocol to Non-interactive Pok
25. 31:23Benchmarks
26. 32:57Apply these constructions

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