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Blind Signatures & Chaumian Ecash Architecture Studio
Model cryptographic privacy in digital bearer assets. Simulate David Chaum blind RSA, elliptic curve Blind Diffie-Hellman Key Exchange (BDHKE / Cashu), cryptographic unlinkability, and double-spend nullifier sets.
Chaumian Ecash
Blind Signatures
BDHKE secp256k1
Spent Nullifiers
Blind signature algorithm and key agreement
Mint keyset denomination identifier
Volume of indistinguishable unspent tokens
Adversarial surveillance and attack scenario
3-Party Ecash Protocol Lifecycle: Alice (Withdrawer) -> Mint -> Carol (Redeemer)
Current Phase
1. Generate Secret
x = random_scalar()
Unlinkability Guarantee
100% Blind
Information-Theoretic Privacy
Spent Nullifier Check
Unspent
O(1) Hash Table Lookup
Token Size
65 Bytes
(x: 32B, C: 33B Point)
Settlement Latency
1.2 ms
Zero Blockchain Confirmation
Anonymity Pool
5,000
Indistinguishable Notes
Live BDHKE Elliptic Curve Mathematical State Trace
| Step Name | Actor | Mathematical Operation | Payload Transmitted | Mint Visibility |
|---|---|---|---|---|
| 1. Blinding | Alice (Client) | B_prime = Y + r * G | B_prime (33-byte Point) | Sees only B_prime (Randomized) |
| 2. Blind Signing | Bob (Mint) | C_prime = k * B_prime | C_prime (33-byte Point) | Deducts balance, signs blindly |
| 3. Unblinding | Alice (Client) | C = C_prime - r * K = k * Y | Local unblinding (Private) | Never sees C or x during withdrawal |
| 4. Redemption | Carol (Recipient) | Verify C == k * hash_to_curve(x) | Token (x, C) | Cannot correlate to Alice's B_prime! |
Production Ecash Implementation (Rust & Python)
Chaumian Ecash Cryptographic Foundations
1. Perfect Blinding Mathematics
Because the blinding factor \(r\) is chosen uniformly at random from \(\mathbb{F}_q\), the blinded point \(B' = Y + rG\) is computationally indistinguishable from a random elliptic curve point. No amount of supercomputing power allows the mint to correlate \(B'\) with \(Y\).
2. Discrete Log Equality (DLEQ) Proofs
To prevent the mint from issuing invalid signatures or utilizing different private keys for different users (a deanonymization attack called key-tagging), modern mints return a DLEQ zero-knowledge proof showing that \(\log_G(K) = \log_{B'}(C')\).
3. Asymmetric Privacy vs Auditing
Ecash provides total consumer privacy (recipients and payers are untraceable), yet the mint remains 100% auditable: proof of reserves on Bitcoin or Lightning ensures the total outstanding token supply equals collateral in escrow.
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