Update README: pivot to Schnorr, drop ECDSA

1 files changed, 37 insertions, 35 deletions

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 # secp256k1 from Scratch — Learning Plan
 
-Building ECDSA on secp256k1 in Go, from first principles.
+Building Schnorr signatures on secp256k1 in Go, from first principles.
 
-**Goal:** Understand the math deeply, not just copy formulas. End with a working (non-production) implementation.
+**Goal:** Understand the math deeply, not just copy formulas. End with a working (non-production) implementation compatible with Bitcoin Taproot and Nostr.
 
 ---
 
@@ -14,57 +14,59 @@ Building ECDSA on secp256k1 in Go, from first principles.
 - [x] **What is an elliptic curve** — y² = x³ + 7, points as (x, y) pairs
 
 ### Part 2: Curve Operations
-- [ ] **Point addition** — adding two points geometrically and algebraically
-- [ ] **Point doubling** — special case when adding a point to itself
-- [ ] **The point at infinity** — identity element (like zero for addition)
-- [ ] **Scalar multiplication** — multiplying a point by an integer (repeated addition)
+- [x] **Point addition** — adding two points geometrically and algebraically
+- [x] **Point doubling** — special case when adding a point to itself
+- [x] **The point at infinity** — identity element (like zero for addition)
+- [x] **Scalar multiplication** — multiplying a point by an integer (repeated addition)
 
 ### Part 3: Key Pairs
-- [ ] **Generator point G** — the "starting point" everyone uses
-- [ ] **Private key** — just a random big number
-- [ ] **Public key** — private key × G (scalar multiplication)
-- [ ] **Why it's hard to reverse** — the discrete log problem
+- [x] **Generator point G** — the "starting point" everyone uses
+- [x] **Private key** — just a random big number
+- [x] **Public key** — private key × G (scalar multiplication)
+- [x] **Why it's hard to reverse** — the discrete log problem
+
+### Part 4: Schnorr Signatures (BIP-340)
+- [ ] **X-only public keys** — 32 bytes, implicit even y
+- [ ] **The signing algorithm** — nonce, challenge, response
+- [ ] **Why random nonce matters** — reuse = leaked private key
+- [ ] **The verification equation** — checking without knowing the private key
+- [ ] **Tagged hashes** — domain separation for security
 
-### Part 4: ECDSA Signing
-- [ ] **What a signature proves** — "I know the private key for this public key"
-- [ ] **The signing algorithm** — k, r, s explained
-- [ ] **Why random k matters** — reuse = leaked private key
+### Part 5: Serialization
+- [ ] **Bech32 encoding** — human-readable format (npub, nsec)
+- [ ] **Hex and bytes** — raw formats
 
-### Part 5: ECDSA Verification
-- [ ] **The verification equation** — checking without knowing the private key
-- [ ] **Putting it together** — sign and verify a message
+---
 
-### Part 6: Implementation
-- [ ] **Field element type** — big.Int wrapper with mod p
-- [ ] **Point type** — x, y coordinates + infinity
-- [ ] **Point addition/doubling** — the core math
-- [ ] **Scalar multiplication** — double-and-add algorithm
-- [ ] **ECDSA sign/verify** — the full flow
-- [ ] **Test against known vectors** — verify correctness
+## Files
+
+| File | Description |
+|------|-------------|
+| `field.go` | Modular arithmetic (mod p) |
+| `point.go` | Curve points and operations |
+| `keys.go` | Private/public key generation |
+| `schnorr.go` | Schnorr signing and verification (TODO) |
 
 ---
 
-## Code Location
+## Compatibility
 
-`/home/ai/vault/projects/secp256k1-learn/`
+This implementation targets:
+- **Bitcoin Taproot** (BIP-340 Schnorr)
+- **Nostr** (NIP-01 uses BIP-340)
 
-We'll build incrementally:
-- `field.go` — modular arithmetic
-- `point.go` — curve points and operations
-- `ecdsa.go` — signing and verification
-- `main.go` — demo/test harness
+Not implemented: ECDSA (used by legacy Bitcoin, Ethereum)
 
 ---
 
 ## Resources
 
+- [BIP-340: Schnorr Signatures](https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki)
 - secp256k1 parameters: p, n, G coordinates
-- Test vectors from Bitcoin/Nostr for verification
-- No external crypto libraries (that's the point)
+- Test vectors from BIP-340 for verification
 
 ---
 
 ## Notes
 
-*Add observations, "aha" moments, or questions here as we go.*
-
+*Learning project — do not use for real money or keys.*