BIP-374: treat challenge hash result e as scalar

bip-0374.mediawiki

@@ -11,7 +11,7 @@
   License: BSD-2-Clause
   Discussion: https://gist.github.com/andrewtoth/df97c3260cc8d12f09d3855ee61322ea
               https://groups.google.com/g/bitcoindev/c/MezoKV5md7s
-  Version: 0.2.0
+  Version: 0.3.0
 </pre>
 
 == Introduction ==
@@ -79,7 +79,7 @@ The algorithm ''GenerateProof(a, B, r, G, m)'' is defined as:
 * Fail if ''k = 0''.
 * Let ''R<sub>1</sub> = k⋅G''.
 * Let ''R<sub>2</sub> = k⋅B''.
-* Let ''e = int(hash<sub>BIP0374/challenge</sub>(cbytes(A) || cbytes(B) || cbytes(C) || cbytes(G) || cbytes(R<sub>1</sub>) || cbytes(R<sub>2</sub>) || m'))''.
+* Let ''e = int(hash<sub>BIP0374/challenge</sub>(cbytes(A) || cbytes(B) || cbytes(C) || cbytes(G) || cbytes(R<sub>1</sub>) || cbytes(R<sub>2</sub>) || m')) mod n''.
 * Let ''s = (k + e⋅a) mod n''.
 * Let ''proof = bytes(32, e) || bytes(32, s)''.
 * If ''VerifyProof(A, B, C, proof, G, m)'' (see below) returns failure, abort.
@@ -99,14 +99,14 @@ Input:
 
 The algorithm ''VerifyProof(A, B, C, proof, G, m)'' is defined as:
 * Fail if any of ''is_infinite(A)'', ''is_infinite(B)'', ''is_infinite(C)'', ''is_infinite(G)''
-* Let ''e = int(proof[0:32])''.
+* Let ''e = int(proof[0:32])''; fail if ''e &ge; n''.
 * Let ''s = int(proof[32:64])''; fail if ''s &ge; n''.
 * Let ''R<sub>1</sub> = s⋅G - e⋅A''.
 * Fail if ''is_infinite(R<sub>1</sub>)''.
 * Let ''R<sub>2</sub> = s⋅B - e⋅C''.
 * Fail if ''is_infinite(R<sub>2</sub>)''.
 * Let ''m' = m if m is provided, otherwise an empty byte array''.
-* Fail if ''e ≠ int(hash<sub>BIP0374/challenge</sub>(cbytes(A) || cbytes(B) || cbytes(C) || cbytes(G) || cbytes(R<sub>1</sub>) || cbytes(R<sub>2</sub>) || m'))''.
+* Fail if ''e ≠ int(hash<sub>BIP0374/challenge</sub>(cbytes(A) || cbytes(B) || cbytes(C) || cbytes(G) || cbytes(R<sub>1</sub>) || cbytes(R<sub>2</sub>) || m')) mod n''.
 * Return success iff no failure occurred before reaching this point.
 
 ==Backwards Compatibility==
@@ -124,6 +124,8 @@ Test vectors can be generated by running <code>./bip-0374/gen_test_vectors.py</c
 
 == Changelog ==
 
+* 0.3.0 (2026-08-19):
+** Treat the challenge ''e'' as a scalar (reduced modulo the curve order) and reject proofs with ''e &ge; n''
 * 0.2.0 (2025-02-27):
 ** Add the message to the rand computation
 * 0.1.0 (2024-12-26):

bip-0374/gen_test_vectors.py

@@ -116,6 +116,19 @@ def gen_all_verify_proof_vectors(f):
                      C.to_bytes_compressed().hex(), proof.hex(), msg_damaged.hex(), "FALSE", f"Tampered message (random bit-flip)"))
     idx += 1
 
+    # out-of-range proof values should fail (e and s must both be valid scalars)
+    order_bytes = GE.ORDER.to_bytes(32, "big")
+    proof_e_out_of_range = order_bytes + proof[32:]
+    assert not dleq_verify_proof(A, B, C, proof_e_out_of_range, G=G, m=msg)
+    writer.writerow((idx, G.to_bytes_compressed().hex(), A.to_bytes_compressed().hex(), B.to_bytes_compressed().hex(),
+                     C.to_bytes_compressed().hex(), proof_e_out_of_range.hex(), msg.hex(), "FALSE", f"Proof with e equal to curve order"))
+    idx += 1
+    proof_s_out_of_range = proof[:32] + order_bytes
+    assert not dleq_verify_proof(A, B, C, proof_s_out_of_range, G=G, m=msg)
+    writer.writerow((idx, G.to_bytes_compressed().hex(), A.to_bytes_compressed().hex(), B.to_bytes_compressed().hex(),
+                     C.to_bytes_compressed().hex(), proof_s_out_of_range.hex(), msg.hex(), "FALSE", f"Proof with s equal to curve order"))
+    idx += 1
+
 
 if __name__ == "__main__":
     print(f"Generating {FILENAME_GENERATE_PROOF_TEST}...")

bip-0374/reference.py

@@ -36,7 +36,7 @@ def dleq_challenge(
             + m,
         ),
         "big",
-    )
+    ) % GE.ORDER
 
 
 def dleq_generate_proof(
@@ -76,6 +76,8 @@ def dleq_verify_proof(
         return False
     assert len(proof) == 64
     e = int.from_bytes(proof[:32], "big")
+    if e >= GE.ORDER:
+        return False
     s = int.from_bytes(proof[32:], "big")
     if s >= GE.ORDER:
         return False

bip-0374/test_vectors_verify_proof.csv

@@ -14,3 +14,5 @@ index,point_G,point_A,point_B,point_C,proof,message,result_success,comment
 12,0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798,03d9a98624c0c74fc7eebd39ed84175f80d03c774908e75ca737a0745d1c64e20a,021cb81121a00f89769903305a367ad3cc02d5b402b12c026e06ac94bde28cd608,03611410561c35dae13135e4ad8094baac9bbcf2f4e18498181a8ff8a6d43be9d9,78a5544afa75bf152653fe55fb76926f2f65131bf090972a0b0b37d310c28a6bde0e7bfacc10ac12d36f55316ba134b6ba0b844a65ae05cad53c0b296c6639bb,22616bb5fb2d7c68270f305122f2a09e833239c4b1c9a04e285119fb606ac794,FALSE,Swapped points case 5
 13,0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798,03611410561c35dae13135e4ad8094baac9bbcf2f4e18498181a8ff8a6d43be9d9,021cb81121a00f89769903305a367ad3cc02d5b402b12c026e06ac94bde28cd608,03d9a98624c0c74fc7eebd39ed84175f80d03c774908e75ca737a0745d1c64e20a,78a5544afa75bf152653fe55fb76926f2f65131ff090972a0b0b37d310c28a6bde0e7bfacc10ac12d36f55316ba134b6ba0b844a65ae05cad53c0b296c6639bb,22616bb5fb2d7c68270f305122f2a09e833239c4b1c9a04e285119fb606ac794,FALSE,Tampered proof (random bit-flip)
 14,0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798,03611410561c35dae13135e4ad8094baac9bbcf2f4e18498181a8ff8a6d43be9d9,021cb81121a00f89769903305a367ad3cc02d5b402b12c026e06ac94bde28cd608,03d9a98624c0c74fc7eebd39ed84175f80d03c774908e75ca737a0745d1c64e20a,78a5544afa75bf152653fe55fb76926f2f65131bf090972a0b0b37d310c28a6bde0e7bfacc10ac12d36f55316ba134b6ba0b844a65ae05cad53c0b296c6639bb,22616bb5fb6d7c68270f305122f2a09e833239c4b1c9a04e285119fb606ac794,FALSE,Tampered message (random bit-flip)
+15,0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798,03611410561c35dae13135e4ad8094baac9bbcf2f4e18498181a8ff8a6d43be9d9,021cb81121a00f89769903305a367ad3cc02d5b402b12c026e06ac94bde28cd608,03d9a98624c0c74fc7eebd39ed84175f80d03c774908e75ca737a0745d1c64e20a,fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141de0e7bfacc10ac12d36f55316ba134b6ba0b844a65ae05cad53c0b296c6639bb,22616bb5fb2d7c68270f305122f2a09e833239c4b1c9a04e285119fb606ac794,FALSE,Proof with e equal to curve order
+16,0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798,03611410561c35dae13135e4ad8094baac9bbcf2f4e18498181a8ff8a6d43be9d9,021cb81121a00f89769903305a367ad3cc02d5b402b12c026e06ac94bde28cd608,03d9a98624c0c74fc7eebd39ed84175f80d03c774908e75ca737a0745d1c64e20a,78a5544afa75bf152653fe55fb76926f2f65131bf090972a0b0b37d310c28a6bfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141,22616bb5fb2d7c68270f305122f2a09e833239c4b1c9a04e285119fb606ac794,FALSE,Proof with s equal to curve order