NUT12: test vectors (cashubtc#105)

* chore: Add hash_e description

* tests(NUT12): DLEQ BlindSignature and hash_e test vector

* tests: DLEQ of proof test vector

* chore: format

Author: thesimplekid

12.md

@@ -32,6 +32,21 @@ e == hash(R1,R2,A,C')
 If true, a in A = a*G must be equal to a in C' = a*B'
 ```
 
+### `hash(x: <Array<[PublicKey]>) -> bytes`
+
+The hash(x) function generates a deterministic Sha256 hash for a given input list of `PublicKey`. The uncompressed hexadecimal representations of each `PublicKey` is concatenated before taking the Sha256 hash.
+
+```python
+def hash_e(*publickeys: PublicKey) -> bytes:
+    e_ = ""
+    for p in publickeys:
+        _p = p.serialize(compressed=False).hex()
+        e_ += str(_p)
+    e = hashlib.sha256(e_.encode("utf-8")).digest()
+    return e
+
+```
+
 ### Mint to user: DLEQ in `BlindSignature`
 
 The mint produces these DLEQ proofs when returning `BlindSignature`'s in the responses for minting ([NUT-04][04]) and swapping ([NUT-03][03]) tokens. The `BlindSignature` object is extended in the following way to include the DLEQ proof:

tests/12-tests.md

@@ -0,0 +1,56 @@
+# NUT-12 Test vectors
+
+## `hash_e` function
+
+```shell
+R1: "020000000000000000000000000000000000000000000000000000000000000001"
+R2: "020000000000000000000000000000000000000000000000000000000000000001"
+K: "020000000000000000000000000000000000000000000000000000000000000001"
+C_: "02a9acc1e48c25eeeb9289b5031cc57da9fe72f3fe2861d264bdc074209b107ba2"
+```
+
+```shell
+hash(R1, R2, K, C_): "a4dc034b74338c28c6bc3ea49731f2a24440fc7c4affc08b31a93fc9fbe6401e"
+```
+
+## DLEQ verification on `BlindSignature`
+
+The following is a `BlindSignature` with a **valid** DLEQ proof.
+```shell
+A: "0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798"
+B_: "02a9acc1e48c25eeeb9289b5031cc57da9fe72f3fe2861d264bdc074209b107ba2"
+```
+
+```json
+{
+  "amount": 8,
+  "id": "00882760bfa2eb41",
+  "C_": "02a9acc1e48c25eeeb9289b5031cc57da9fe72f3fe2861d264bdc074209b107ba2",
+  "dleq": {
+    "e": "9818e061ee51d5c8edc3342369a554998ff7b4381c8652d724cdf46429be73d9",
+    "s": "9818e061ee51d5c8edc3342369a554998ff7b4381c8652d724cdf46429be73da"
+  }
+}
+```
+
+## DLEQ verification on `Proof`
+
+The following is a `Prood` with a **valid** DLEQ proof.
+
+```shell
+A: "0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798"
+```
+
+```json
+{
+  "amount": 1,
+  "id": "00882760bfa2eb41",
+  "secret": "daf4dd00a2b68a0858a80450f52c8a7d2ccf87d375e43e216e0c571f089f63e9",
+  "C": "024369d2d22a80ecf78f3937da9d5f30c1b9f74f0c32684d583cca0fa6a61cdcfc",
+  "dleq": {
+    "e": "b31e58ac6527f34975ffab13e70a48b6d2b0d35abc4b03f0151f09ee1a9763d4",
+    "s": "8fbae004c59e754d71df67e392b6ae4e29293113ddc2ec86592a0431d16306d8",
+    "r": "a6d13fcd7a18442e6076f5e1e7c887ad5de40a019824bdfa9fe740d302e8d861"
+  }
+}
+```