Merge pull request #893 from sipa/bip-taproot

BIP 340 improvements

3 files changed, 213 insertions, 122 deletions

diff --git a/bip-0340/reference.py b/bip-0340/reference.py
index f2a944f..f24963c 100644
--- a/bip-0340/reference.py
+++ b/bip-0340/reference.py
@@ -1,6 +1,16 @@
+from typing import Tuple, Optional, Any
 import hashlib
 import binascii
 
+# Set DEBUG to True to get a detailed debug output including
+# intermediate values during key generation, signing, and
+# verification. This is implemented via calls to the
+# debug_print_vars() function.
+#
+# If you want to print values on an individual basis, use
+# the pretty() function, e.g., print(pretty(foo)).
+DEBUG = False
+
 p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F
 n = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141
 
@@ -8,50 +18,55 @@ n = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141
 # represented by the None keyword.
 G = (0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798, 0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8)
 
+Point = Tuple[int, int]
+
 # This implementation can be sped up by storing the midstate after hashing
 # tag_hash instead of rehashing it all the time.
-def tagged_hash(tag, msg):
+def tagged_hash(tag: str, msg: bytes) -> bytes:
     tag_hash = hashlib.sha256(tag.encode()).digest()
     return hashlib.sha256(tag_hash + tag_hash + msg).digest()
 
-def is_infinity(P):
+def is_infinity(P: Optional[Point]) -> bool:
     return P is None
 
-def x(P):
+def x(P: Point) -> int:
     return P[0]
 
-def y(P):
+def y(P: Point) -> int:
     return P[1]
 
-def point_add(P1, P2):
-    if (P1 is None):
+def point_add(P1: Optional[Point], P2: Optional[Point]) -> Optional[Point]:
+    if P1 is None:
         return P2
-    if (P2 is None):
+    if P2 is None:
         return P1
-    if (x(P1) == x(P2) and y(P1) != y(P2)):
+    if (x(P1) == x(P2)) and (y(P1) != y(P2)):
         return None
-    if (P1 == P2):
+    if P1 == P2:
         lam = (3 * x(P1) * x(P1) * pow(2 * y(P1), p - 2, p)) % p
     else:
         lam = ((y(P2) - y(P1)) * pow(x(P2) - x(P1), p - 2, p)) % p
     x3 = (lam * lam - x(P1) - x(P2)) % p
     return (x3, (lam * (x(P1) - x3) - y(P1)) % p)
 
-def point_mul(P, n):
+def point_mul(P: Optional[Point], n: int) -> Optional[Point]:
     R = None
     for i in range(256):
-        if ((n >> i) & 1):
+        if (n >> i) & 1:
             R = point_add(R, P)
         P = point_add(P, P)
     return R
 
-def bytes_from_int(x):
+def bytes_from_int(x: int) -> bytes:
     return x.to_bytes(32, byteorder="big")
 
-def bytes_from_point(P):
+def bytes_from_point(P: Point) -> bytes:
     return bytes_from_int(x(P))
 
-def point_from_bytes(b):
+def xor_bytes(b0: bytes, b1: bytes) -> bytes:
+    return bytes(x ^ y for (x, y) in zip(b0, b1))
+
+def lift_x_square_y(b: bytes) -> Optional[Point]:
     x = int_from_bytes(b)
     if x >= p:
         return None
@@ -59,94 +74,125 @@ def point_from_bytes(b):
     y = pow(y_sq, (p + 1) // 4, p)
     if pow(y, 2, p) != y_sq:
         return None
-    return [x, y]
+    return (x, y)
+
+def lift_x_even_y(b: bytes) -> Optional[Point]:
+    P = lift_x_square_y(b)
+    if P is None:
+        return None
+    else:
+        return (x(P), y(P) if y(P) % 2 == 0 else p - y(P))
 
-def int_from_bytes(b):
+def int_from_bytes(b: bytes) -> int:
     return int.from_bytes(b, byteorder="big")
 
-def hash_sha256(b):
+def hash_sha256(b: bytes) -> bytes:
     return hashlib.sha256(b).digest()
 
-def is_square(x):
-    return pow(x, (p - 1) // 2, p) == 1
+def is_square(x: int) -> bool:
+    return int(pow(x, (p - 1) // 2, p)) == 1
 
-def has_square_y(P):
-    return not is_infinity(P) and is_square(y(P))
+def has_square_y(P: Optional[Point]) -> bool:
+    infinity = is_infinity(P)
+    if infinity: return False
+    assert P is not None
+    return is_square(y(P))
 
-def pubkey_gen(seckey):
-    x = int_from_bytes(seckey)
-    if not (1 <= x <= n - 1):
+def has_even_y(P: Point) -> bool:
+    return y(P) % 2 == 0
+
+def pubkey_gen(seckey: bytes) -> bytes:
+    d0 = int_from_bytes(seckey)
+    if not (1 <= d0 <= n - 1):
         raise ValueError('The secret key must be an integer in the range 1..n-1.')
-    P = point_mul(G, x)
+    P = point_mul(G, d0)
+    assert P is not None
     return bytes_from_point(P)
 
-def schnorr_sign(msg, seckey0):
+def schnorr_sign(msg: bytes, seckey: bytes, aux_rand: bytes) -> bytes:
     if len(msg) != 32:
         raise ValueError('The message must be a 32-byte array.')
-    seckey0 = int_from_bytes(seckey0)
-    if not (1 <= seckey0 <= n - 1):
+    d0 = int_from_bytes(seckey)
+    if not (1 <= d0 <= n - 1):
         raise ValueError('The secret key must be an integer in the range 1..n-1.')
-    P = point_mul(G, seckey0)
-    seckey = seckey0 if has_square_y(P) else n - seckey0
-    k0 = int_from_bytes(tagged_hash("BIPSchnorrDerive", bytes_from_int(seckey) + msg)) % n
+    if len(aux_rand) != 32:
+        raise ValueError('aux_rand must be 32 bytes instead of %i.' % len(aux_rand))
+    P = point_mul(G, d0)
+    assert P is not None
+    d = d0 if has_even_y(P) else n - d0
+    t = xor_bytes(bytes_from_int(d), tagged_hash("BIP340/aux", aux_rand))
+    k0 = int_from_bytes(tagged_hash("BIP340/nonce", t + bytes_from_point(P) + msg)) % n
     if k0 == 0:
         raise RuntimeError('Failure. This happens only with negligible probability.')
     R = point_mul(G, k0)
+    assert R is not None
     k = n - k0 if not has_square_y(R) else k0
-    e = int_from_bytes(tagged_hash("BIPSchnorr", bytes_from_point(R) + bytes_from_point(P) + msg)) % n
-    return bytes_from_point(R) + bytes_from_int((k + e * seckey) % n)
-
-def schnorr_verify(msg, pubkey, sig):
+    e = int_from_bytes(tagged_hash("BIP340/challenge", bytes_from_point(R) + bytes_from_point(P) + msg)) % n
+    sig = bytes_from_point(R) + bytes_from_int((k + e * d) % n)
+    debug_print_vars()
+    if not schnorr_verify(msg, bytes_from_point(P), sig):
+        raise RuntimeError('The created signature does not pass verification.')
+    return sig
+
+def schnorr_verify(msg: bytes, pubkey: bytes, sig: bytes) -> bool:
     if len(msg) != 32:
         raise ValueError('The message must be a 32-byte array.')
     if len(pubkey) != 32:
         raise ValueError('The public key must be a 32-byte array.')
     if len(sig) != 64:
         raise ValueError('The signature must be a 64-byte array.')
-    P = point_from_bytes(pubkey)
-    if (P is None):
-        return False
+    P = lift_x_even_y(pubkey)
     r = int_from_bytes(sig[0:32])
     s = int_from_bytes(sig[32:64])
-    if (r >= p or s >= n):
+    if (P is None) or (r >= p) or (s >= n):
+        debug_print_vars()
         return False
-    e = int_from_bytes(tagged_hash("BIPSchnorr", sig[0:32] + pubkey + msg)) % n
+    e = int_from_bytes(tagged_hash("BIP340/challenge", sig[0:32] + pubkey + msg)) % n
     R = point_add(point_mul(G, s), point_mul(P, n - e))
-    if R is None or not has_square_y(R) or x(R) != r:
+    if (R is None) or (not has_square_y(R)) or (x(R) != r):
+        debug_print_vars()
         return False
+    debug_print_vars()
     return True
 
 #
 # The following code is only used to verify the test vectors.
 #
 import csv
+import os
+import sys
 
-def test_vectors():
+def test_vectors() -> bool:
     all_passed = True
-    with open('test-vectors.csv', newline='') as csvfile:
+    with open(os.path.join(sys.path[0], 'test-vectors.csv'), newline='') as csvfile:
         reader = csv.reader(csvfile)
         reader.__next__()
         for row in reader:
-            (index, seckey, pubkey, msg, sig, result, comment) = row
-            pubkey = bytes.fromhex(pubkey)
-            msg = bytes.fromhex(msg)
-            sig = bytes.fromhex(sig)
-            result = result == 'TRUE'
-            print('\nTest vector #%-3i: ' % int(index))
-            if seckey != '':
-                seckey = bytes.fromhex(seckey)
+            (index, seckey_hex, pubkey_hex, aux_rand_hex, msg_hex, sig_hex, result_str, comment) = row
+            pubkey = bytes.fromhex(pubkey_hex)
+            msg = bytes.fromhex(msg_hex)
+            sig = bytes.fromhex(sig_hex)
+            result = result_str == 'TRUE'
+            print('\nTest vector', ('#' + index).rjust(3, ' ') + ':')
+            if seckey_hex != '':
+                seckey = bytes.fromhex(seckey_hex)
                 pubkey_actual = pubkey_gen(seckey)
                 if pubkey != pubkey_actual:
                     print(' * Failed key generation.')
                     print('   Expected key:', pubkey.hex().upper())
                     print('     Actual key:', pubkey_actual.hex().upper())
-                sig_actual = schnorr_sign(msg, seckey)
-                if sig == sig_actual:
-                    print(' * Passed signing test.')
-                else:
-                    print(' * Failed signing test.')
-                    print('   Expected signature:', sig.hex().upper())
-                    print('     Actual signature:', sig_actual.hex().upper())
+                aux_rand = bytes.fromhex(aux_rand_hex)
+                try:
+                    sig_actual = schnorr_sign(msg, seckey, aux_rand)
+                    if sig == sig_actual:
+                        print(' * Passed signing test.')
+                    else:
+                        print(' * Failed signing test.')
+                        print('   Expected signature:', sig.hex().upper())
+                        print('     Actual signature:', sig_actual.hex().upper())
+                        all_passed = False
+                except RuntimeError as e:
+                    print(' * Signing test raised exception:', e)
                     all_passed = False
             result_actual = schnorr_verify(msg, pubkey, sig)
             if result == result_actual:
@@ -165,5 +211,29 @@ def test_vectors():
         print('Some test vectors failed.')
     return all_passed
 
+#
+# The following code is only used for debugging
+#
+import inspect
+
+def pretty(v: Any) -> Any:
+    if isinstance(v, bytes):
+        return '0x' + v.hex()
+    if isinstance(v, int):
+        return pretty(bytes_from_int(v))
+    if isinstance(v, tuple):
+        return tuple(map(pretty, v))
+    return v
+
+def debug_print_vars() -> None:
+    if DEBUG:
+        current_frame = inspect.currentframe()
+        assert current_frame is not None
+        frame = current_frame.f_back
+        assert frame is not None
+        print('   Variables in function ', frame.f_code.co_name, ' at line ', frame.f_lineno, ':', sep='')
+        for var_name, var_val in frame.f_locals.items():
+            print('   ' + var_name.rjust(11, ' '), '==', pretty(var_val))
+
 if __name__ == '__main__':
     test_vectors()
diff --git a/bip-0340/test-vectors.csv b/bip-0340/test-vectors.csv
index 3970803..beaef5a 100644
--- a/bip-0340/test-vectors.csv
+++ b/bip-0340/test-vectors.csv
@@ -1,16 +1,16 @@
-index,secret key,public key,message,signature,verification result,comment

-0,0000000000000000000000000000000000000000000000000000000000000001,79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798,0000000000000000000000000000000000000000000000000000000000000000,528F745793E8472C0329742A463F59E58F3A3F1A4AC09C28F6F8514D4D0322A258BD08398F82CF67B812AB2C7717CE566F877C2F8795C846146978E8F04782AE,TRUE,

-1,B7E151628AED2A6ABF7158809CF4F3C762E7160F38B4DA56A784D9045190CFEF,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,667C2F778E0616E611BD0C14B8A600C5884551701A949EF0EBFD72D452D64E844160BCFC3F466ECB8FACD19ADE57D8699D74E7207D78C6AEDC3799B52A8E0598,TRUE,

-2,C90FDAA22168C234C4C6628B80DC1CD129024E088A67CC74020BBEA63B14E5C9,DD308AFEC5777E13121FA72B9CC1B7CC0139715309B086C960E18FD969774EB8,5E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C,2D941B38E32624BF0AC7669C0971B990994AF6F9B18426BF4F4E7EC10E6CDF386CF646C6DDAFCFA7F1993EEB2E4D66416AEAD1DDAE2F22D63CAD901412D116C6,TRUE,

-3,0B432B2677937381AEF05BB02A66ECD012773062CF3FA2549E44F58ED2401710,25D1DFF95105F5253C4022F628A996AD3A0D95FBF21D468A1B33F8C160D8F517,FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF,8BD2C11604B0A87A443FCC2E5D90E5328F934161B18864FB48CE10CB59B45FB9B5B2A0F129BD88F5BDC05D5C21E5C57176B913002335784F9777A24BD317CD36,TRUE,test fails if msg is reduced modulo p or n

-4,,D69C3509BB99E412E68B0FE8544E72837DFA30746D8BE2AA65975F29D22DC7B9,4DF3C3F68FCC83B27E9D42C90431A72499F17875C81A599B566C9889B9696703,00000000000000000000003B78CE563F89A0ED9414F5AA28AD0D96D6795F9C63EE374AC7FAE927D334CCB190F6FB8FD27A2DDC639CCEE46D43F113A4035A2C7F,TRUE,

-5,,EEFDEA4CDB677750A420FEE807EACF21EB9898AE79B9768766E4FAA04A2D4A34,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,667C2F778E0616E611BD0C14B8A600C5884551701A949EF0EBFD72D452D64E844160BCFC3F466ECB8FACD19ADE57D8699D74E7207D78C6AEDC3799B52A8E0598,FALSE,public key not on the curve

-6,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,F9308A019258C31049344F85F89D5229B531C845836F99B08601F113BCE036F9935554D1AA5F0374E5CDAACB3925035C7C169B27C4426DF0A6B19AF3BAEAB138,FALSE,has_square_y(R) is false

-7,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,10AC49A6A2EBF604189C5F40FC75AF2D42D77DE9A2782709B1EB4EAF1CFE9108D7003B703A3499D5E29529D39BA040A44955127140F81A8A89A96F992AC0FE79,FALSE,negated message

-8,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,667C2F778E0616E611BD0C14B8A600C5884551701A949EF0EBFD72D452D64E84BE9F4303C0B9913470532E6521A827951D39F5C631CFD98CE39AC4D7A5A83BA9,FALSE,negated s value

-9,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,000000000000000000000000000000000000000000000000000000000000000099D2F0EBC2996808208633CD9926BF7EC3DAB73DAAD36E85B3040A698E6D1CE0,FALSE,sG - eP is infinite. Test fails in single verification if has_square_y(inf) is defined as true and x(inf) as 0

-10,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,000000000000000000000000000000000000000000000000000000000000000124E81D89F01304695CE943F7D5EBD00EF726A0864B4FF33895B4E86BEADC5456,FALSE,sG - eP is infinite. Test fails in single verification if has_square_y(inf) is defined as true and x(inf) as 1

-11,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,4A298DACAE57395A15D0795DDBFD1DCB564DA82B0F269BC70A74F8220429BA1D4160BCFC3F466ECB8FACD19ADE57D8699D74E7207D78C6AEDC3799B52A8E0598,FALSE,sig[0:32] is not an X coordinate on the curve

-12,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F4160BCFC3F466ECB8FACD19ADE57D8699D74E7207D78C6AEDC3799B52A8E0598,FALSE,sig[0:32] is equal to field size

-13,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,667C2F778E0616E611BD0C14B8A600C5884551701A949EF0EBFD72D452D64E84FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141,FALSE,sig[32:64] is equal to curve order

-14,,FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC30,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,667C2F778E0616E611BD0C14B8A600C5884551701A949EF0EBFD72D452D64E844160BCFC3F466ECB8FACD19ADE57D8699D74E7207D78C6AEDC3799B52A8E0598,FALSE,public key is not a valid X coordinate because it exceeds the field size

+index,secret key,public key,aux_rand,message,signature,verification result,comment

+0,0000000000000000000000000000000000000000000000000000000000000003,F9308A019258C31049344F85F89D5229B531C845836F99B08601F113BCE036F9,0000000000000000000000000000000000000000000000000000000000000000,0000000000000000000000000000000000000000000000000000000000000000,067E337AD551B2276EC705E43F0920926A9CE08AC68159F9D258C9BBA412781C9F059FCDF4824F13B3D7C1305316F956704BB3FEA2C26142E18ACD90A90C947E,TRUE,

+1,B7E151628AED2A6ABF7158809CF4F3C762E7160F38B4DA56A784D9045190CFEF,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,0000000000000000000000000000000000000000000000000000000000000001,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,0E12B8C520948A776753A96F21ABD7FDC2D7D0C0DDC90851BE17B04E75EF86A47EF0DA46C4DC4D0D1BCB8668C2CE16C54C7C23A6716EDE303AF86774917CF928,TRUE,

+2,C90FDAA22168C234C4C6628B80DC1CD129024E088A67CC74020BBEA63B14E5C9,DD308AFEC5777E13121FA72B9CC1B7CC0139715309B086C960E18FD969774EB8,C87AA53824B4D7AE2EB035A2B5BBBCCC080E76CDC6D1692C4B0B62D798E6D906,7E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C,FC012F9FB8FE00A358F51EF93DCE0DC0C895F6E9A87C6C4905BC820B0C3677616B8737D14E703AF8E16E22E5B8F26227D41E5128F82D86F747244CC289C74D1D,TRUE,

+3,0B432B2677937381AEF05BB02A66ECD012773062CF3FA2549E44F58ED2401710,25D1DFF95105F5253C4022F628A996AD3A0D95FBF21D468A1B33F8C160D8F517,FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF,FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF,FC132D4E426DFF535AEC0FA7083AC5118BC1D5FFFD848ABD8290C23F271CA0DD11AEDCEA3F55DA9BD677FE29C9DDA0CF878BCE43FDE0E313D69D1AF7A5AE8369,TRUE,test fails if msg is reduced modulo p or n

+4,,D69C3509BB99E412E68B0FE8544E72837DFA30746D8BE2AA65975F29D22DC7B9,,4DF3C3F68FCC83B27E9D42C90431A72499F17875C81A599B566C9889B9696703,00000000000000000000003B78CE563F89A0ED9414F5AA28AD0D96D6795F9C630EC50E5363E227ACAC6F542CE1C0B186657E0E0D1A6FFE283A33438DE4738419,TRUE,

+5,,EEFDEA4CDB677750A420FEE807EACF21EB9898AE79B9768766E4FAA04A2D4A34,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,7036D6BFE1837AE919631039A2CF652A295DFAC9A8BBB0806014B2F48DD7C807941607B563ABBA414287F374A332BA3636DE009EE1EF551A17796B72B68B8A24,FALSE,public key not on the curve

+6,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,F9308A019258C31049344F85F89D5229B531C845836F99B08601F113BCE036F995A579DA959FA739FCE39E8BD16FECB5CDCF97060B2C73CDE60E87ABCA1AA5D9,FALSE,has_square_y(R) is false

+7,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,F8704654F4687B7365ED32E796DE92761390A3BCC495179BFE073817B7ED32824E76B987F7C1F9A751EF5C343F7645D3CFFC7D570B9A7192EBF1898E1344E3BF,FALSE,negated message

+8,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,7036D6BFE1837AE919631039A2CF652A295DFAC9A8BBB0806014B2F48DD7C8076BE9F84A9C5445BEBD780C8B5CCD45C883D0DC47CD594B21A858F31A19AAB71D,FALSE,negated s value

+9,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,00000000000000000000000000000000000000000000000000000000000000009915EE59F07F9DBBAEDC31BFCC9B34AD49DE669CD24773BCED77DDA36D073EC8,FALSE,sG - eP is infinite. Test fails in single verification if has_square_y(inf) is defined as true and x(inf) as 0

+10,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,0000000000000000000000000000000000000000000000000000000000000001C7EC918B2B9CF34071BB54BED7EB4BB6BAB148E9A7E36E6B228F95DFA08B43EC,FALSE,sG - eP is infinite. Test fails in single verification if has_square_y(inf) is defined as true and x(inf) as 1

+11,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,4A298DACAE57395A15D0795DDBFD1DCB564DA82B0F269BC70A74F8220429BA1D941607B563ABBA414287F374A332BA3636DE009EE1EF551A17796B72B68B8A24,FALSE,sig[0:32] is not an X coordinate on the curve

+12,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F941607B563ABBA414287F374A332BA3636DE009EE1EF551A17796B72B68B8A24,FALSE,sig[0:32] is equal to field size

+13,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,7036D6BFE1837AE919631039A2CF652A295DFAC9A8BBB0806014B2F48DD7C807FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141,FALSE,sig[32:64] is equal to curve order

+14,,FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC30,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,7036D6BFE1837AE919631039A2CF652A295DFAC9A8BBB0806014B2F48DD7C807941607B563ABBA414287F374A332BA3636DE009EE1EF551A17796B72B68B8A24,FALSE,public key is not a valid X coordinate because it exceeds the field size

diff --git a/bip-0340/test-vectors.py b/bip-0340/test-vectors.py
index 195b61b..9c029ec 100644
--- a/bip-0340/test-vectors.py
+++ b/bip-0340/test-vectors.py
@@ -2,46 +2,67 @@ import sys
 from reference import *
 
 def vector0():
-    seckey = bytes_from_int(1)
+    seckey = bytes_from_int(3)
     msg = bytes_from_int(0)
-    sig = schnorr_sign(msg, seckey)
+    aux_rand = bytes_from_int(0)
+    sig = schnorr_sign(msg, seckey, aux_rand)
     pubkey = pubkey_gen(seckey)
 
-    # The point reconstructed from the public key has an even Y coordinate.
-    pubkey_point = point_from_bytes(pubkey)
-    assert(pubkey_point[1] & 1 == 0)
+    # We should have at least one test vector where the seckey needs to be
+    # negated and one where it doesn't. In this one the seckey doesn't need to
+    # be negated.
+    x = int_from_bytes(seckey)
+    P = point_mul(G, x)
+    assert(y(P) % 2 == 0)
 
-    return (seckey, pubkey, msg, sig, "TRUE", None)
+    # For historical reasons (pubkey tiebreaker was squareness and not evenness)
+    # we should have at least one test vector where the the point reconstructed
+    # from the public key has a square and one where it has a non-square Y
+    # coordinate. In this one Y is non-square.
+    pubkey_point = lift_x_even_y(pubkey)
+    assert(not has_square_y(pubkey_point))
+
+    return (seckey, pubkey, aux_rand, msg, sig, "TRUE", None)
 
 def vector1():
     seckey = bytes_from_int(0xB7E151628AED2A6ABF7158809CF4F3C762E7160F38B4DA56A784D9045190CFEF)
     msg = bytes_from_int(0x243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89)
-    sig = schnorr_sign(msg, seckey)
-    pubkey = pubkey_gen(seckey)
-
-    # The point reconstructed from the public key has an odd Y coordinate.
-    pubkey_point = point_from_bytes(pubkey)
-    assert(pubkey_point[1] & 1 == 1)
+    aux_rand = bytes_from_int(1)
 
-    return (seckey, pubkey, msg, sig, "TRUE", None)
+    sig = schnorr_sign(msg, seckey, aux_rand)
+    return (seckey, pubkey_gen(seckey), aux_rand, msg, sig, "TRUE", None)
 
 def vector2():
     seckey = bytes_from_int(0xC90FDAA22168C234C4C6628B80DC1CD129024E088A67CC74020BBEA63B14E5C9)
-    msg = bytes_from_int(0x5E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C)
-    sig = schnorr_sign(msg, seckey)
+    msg = bytes_from_int(0x7E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C)
+    aux_rand = bytes_from_int(0xC87AA53824B4D7AE2EB035A2B5BBBCCC080E76CDC6D1692C4B0B62D798E6D906)
+    sig = schnorr_sign(msg, seckey, aux_rand)
+
+    # The point reconstructed from the public key has a square Y coordinate.
+    pubkey = pubkey_gen(seckey)
+    pubkey_point = lift_x_even_y(pubkey)
+    assert(has_square_y(pubkey_point))
 
     # This signature vector would not verify if the implementer checked the
     # squareness of the X coordinate of R instead of the Y coordinate.
-    R = point_from_bytes(sig[0:32])
+    R = lift_x_square_y(sig[0:32])
     assert(not is_square(R[0]))
 
-    return (seckey, pubkey_gen(seckey), msg, sig, "TRUE", None)
+    return (seckey, pubkey, aux_rand, msg, sig, "TRUE", None)
 
 def vector3():
     seckey = bytes_from_int(0x0B432B2677937381AEF05BB02A66ECD012773062CF3FA2549E44F58ED2401710)
+
+    # Need to negate this seckey before signing
+    x = int_from_bytes(seckey)
+    P = point_mul(G, x)
+    assert(y(P) % 2 != 0)
+
     msg = bytes_from_int(0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)
-    sig = schnorr_sign(msg, seckey)
-    return (seckey, pubkey_gen(seckey), msg, sig, "TRUE", "test fails if msg is reduced modulo p or n")
+    aux_rand = bytes_from_int(0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)
+
+    sig = schnorr_sign(msg, seckey, aux_rand)
+    return (seckey, pubkey_gen(seckey), aux_rand, msg, sig, "TRUE", "test fails if msg is reduced modulo p or n")
 
 # Signs with a given nonce. This can be INSECURE and is only INTENDED FOR
 # GENERATING TEST VECTORS. Results in an invalid signature if y(kG) is not
@@ -53,9 +74,9 @@ def insecure_schnorr_sign_fixed_nonce(msg, seckey0, k):
     if not (1 <= seckey0 <= n - 1):
         raise ValueError('The secret key must be an integer in the range 1..n-1.')
     P = point_mul(G, seckey0)
-    seckey = seckey0 if has_square_y(P) else n - seckey0
+    seckey = seckey0 if has_even_y(P) else n - seckey0
     R = point_mul(G, k)
-    e = int_from_bytes(tagged_hash("BIPSchnorr", bytes_from_point(R) + bytes_from_point(P) + msg)) % n
+    e = int_from_bytes(tagged_hash("BIP340/challenge", bytes_from_point(R) + bytes_from_point(P) + msg)) % n
     return bytes_from_point(R) + bytes_from_int((k + e * seckey) % n)
 
 # Creates a singature with a small x(R) by using k = 1/2
@@ -64,10 +85,11 @@ def vector4():
     seckey = bytes_from_int(0x763758E5CBEEDEE4F7D3FC86F531C36578933228998226672F13C4F0EBE855EB)
     msg = bytes_from_int(0x4DF3C3F68FCC83B27E9D42C90431A72499F17875C81A599B566C9889B9696703)
     sig = insecure_schnorr_sign_fixed_nonce(msg, seckey, one_half)
-    return (None, pubkey_gen(seckey), msg, sig, "TRUE", None)
+    return (None, pubkey_gen(seckey), None, msg, sig, "TRUE", None)
 
 default_seckey = bytes_from_int(0xB7E151628AED2A6ABF7158809CF4F3C762E7160F38B4DA56A784D9045190CFEF)
 default_msg = bytes_from_int(0x243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89)
+default_aux_rand = bytes_from_int(0xC87AA53824B4D7AE2EB035A2B5BBBCCC080E76CDC6D1692C4B0B62D798E6D906)
 
 # Public key is not on the curve
 def vector5():
@@ -75,12 +97,12 @@ def vector5():
     # public key.
     seckey = default_seckey
     msg = default_msg
-    sig = schnorr_sign(msg, seckey)
+    sig = schnorr_sign(msg, seckey, default_aux_rand)
 
     pubkey = bytes_from_int(0xEEFDEA4CDB677750A420FEE807EACF21EB9898AE79B9768766E4FAA04A2D4A34)
-    assert(point_from_bytes(pubkey) is None)
+    assert(lift_x_even_y(pubkey) is None)
 
-    return (None, pubkey, msg, sig, "FALSE", "public key not on the curve")
+    return (None, pubkey, None, msg, sig, "FALSE", "public key not on the curve")
 
 def vector6():
     seckey = default_seckey
@@ -92,21 +114,21 @@ def vector6():
     R = point_mul(G, k)
     assert(not has_square_y(R))
 
-    return (None, pubkey_gen(seckey), msg, sig, "FALSE", "has_square_y(R) is false")
+    return (None, pubkey_gen(seckey), None, msg, sig, "FALSE", "has_square_y(R) is false")
 
 def vector7():
     seckey = default_seckey
     msg = int_from_bytes(default_msg)
     neg_msg = bytes_from_int(n - msg)
-    sig = schnorr_sign(neg_msg, seckey)
-    return (None, pubkey_gen(seckey), bytes_from_int(msg), sig, "FALSE", "negated message")
+    sig = schnorr_sign(neg_msg, seckey, default_aux_rand)
+    return (None, pubkey_gen(seckey), None, bytes_from_int(msg), sig, "FALSE", "negated message")
 
 def vector8():
     seckey = default_seckey
     msg = default_msg
-    sig = schnorr_sign(msg, seckey)
+    sig = schnorr_sign(msg, seckey, default_aux_rand)
     sig = sig[0:32] + bytes_from_int(n - int_from_bytes(sig[32:64]))
-    return (None, pubkey_gen(seckey), msg, sig, "FALSE", "negated s value")
+    return (None, pubkey_gen(seckey), None, msg, sig, "FALSE", "negated s value")
 
 def bytes_from_point_inf0(P):
     if P == None:
@@ -125,7 +147,7 @@ def vector9():
     sig = insecure_schnorr_sign_fixed_nonce(msg, seckey, k)
     bytes_from_point.__code__ = bytes_from_point_tmp
 
-    return (None, pubkey_gen(seckey), msg, sig, "FALSE", "sG - eP is infinite. Test fails in single verification if has_square_y(inf) is defined as true and x(inf) as 0")
+    return (None, pubkey_gen(seckey), None, msg, sig, "FALSE", "sG - eP is infinite. Test fails in single verification if has_square_y(inf) is defined as true and x(inf) as 0")
 
 def bytes_from_point_inf1(P):
     if P == None:
@@ -144,7 +166,7 @@ def vector10():
     sig = insecure_schnorr_sign_fixed_nonce(msg, seckey, k)
     bytes_from_point.__code__ = bytes_from_point_tmp
 
-    return (None, pubkey_gen(seckey), msg, sig, "FALSE", "sG - eP is infinite. Test fails in single verification if has_square_y(inf) is defined as true and x(inf) as 1")
+    return (None, pubkey_gen(seckey), None, msg, sig, "FALSE", "sG - eP is infinite. Test fails in single verification if has_square_y(inf) is defined as true and x(inf) as 1")
 
 # It's cryptographically impossible to create a test vector that fails if run
 # in an implementation which merely misses the check that sig[0:32] is an X
@@ -152,14 +174,14 @@ def vector10():
 def vector11():
     seckey = default_seckey
     msg = default_msg
-    sig = schnorr_sign(msg, seckey)
+    sig = schnorr_sign(msg, seckey, default_aux_rand)
 
     # Replace R's X coordinate with an X coordinate that's not on the curve
     x_not_on_curve = bytes_from_int(0x4A298DACAE57395A15D0795DDBFD1DCB564DA82B0F269BC70A74F8220429BA1D)
-    assert(point_from_bytes(x_not_on_curve) is None)
+    assert(lift_x_square_y(x_not_on_curve) is None)
     sig = x_not_on_curve + sig[32:64]
 
-    return (None, pubkey_gen(seckey), msg, sig, "FALSE", "sig[0:32] is not an X coordinate on the curve")
+    return (None, pubkey_gen(seckey), None, msg, sig, "FALSE", "sig[0:32] is not an X coordinate on the curve")
 
 # It's cryptographically impossible to create a test vector that fails if run
 # in an implementation which merely misses the check that sig[0:32] is smaller
@@ -167,12 +189,12 @@ def vector11():
 def vector12():
     seckey = default_seckey
     msg = default_msg
-    sig = schnorr_sign(msg, seckey)
+    sig = schnorr_sign(msg, seckey, default_aux_rand)
 
     # Replace R's X coordinate with an X coordinate that's equal to field size
     sig = bytes_from_int(p) + sig[32:64]
 
-    return (None, pubkey_gen(seckey), msg, sig, "FALSE", "sig[0:32] is equal to field size")
+    return (None, pubkey_gen(seckey), None, msg, sig, "FALSE", "sig[0:32] is equal to field size")
 
 # It's cryptographically impossible to create a test vector that fails if run
 # in an implementation which merely misses the check that sig[32:64] is smaller
@@ -180,12 +202,12 @@ def vector12():
 def vector13():
     seckey = default_seckey
     msg = default_msg
-    sig = schnorr_sign(msg, seckey)
+    sig = schnorr_sign(msg, seckey, default_aux_rand)
 
     # Replace s with a number that's equal to the curve order
     sig = sig[0:32] + bytes_from_int(n)
 
-    return (None, pubkey_gen(seckey), msg, sig, "FALSE", "sig[32:64] is equal to curve order")
+    return (None, pubkey_gen(seckey), None, msg, sig, "FALSE", "sig[32:64] is equal to curve order")
 
 # Test out of range pubkey
 # It's cryptographically impossible to create a test vector that fails if run
@@ -197,16 +219,15 @@ def vector14():
     # public key.
     seckey = default_seckey
     msg = default_msg
-    sig = schnorr_sign(msg, seckey)
-
+    sig = schnorr_sign(msg, seckey, default_aux_rand)
     pubkey_int = p + 1
     pubkey = bytes_from_int(pubkey_int)
-    assert(point_from_bytes(pubkey) is None)
+    assert(lift_x_even_y(pubkey) is None)
     # If an implementation would reduce a given public key modulo p then the
     # pubkey would be valid
-    assert(point_from_bytes(bytes_from_int(pubkey_int % p)) is not None)
+    assert(lift_x_even_y(bytes_from_int(pubkey_int % p)) is not None)
 
-    return (None, pubkey, msg, sig, "FALSE", "public key is not a valid X coordinate because it exceeds the field size")
+    return (None, pubkey, None, msg, sig, "FALSE", "public key is not a valid X coordinate because it exceeds the field size")
 
 vectors = [
         vector0(),
@@ -227,14 +248,14 @@ vectors = [
     ]
 
 # Converts the byte strings of a test vector into hex strings
-def bytes_to_hex(seckey, pubkey, msg, sig, result, comment):
-    return (seckey.hex().upper() if seckey is not None else None, pubkey.hex().upper(), msg.hex().upper(), sig.hex().upper(), result, comment)
+def bytes_to_hex(seckey, pubkey, aux_rand, msg, sig, result, comment):
+    return (seckey.hex().upper() if seckey is not None else None, pubkey.hex().upper(), aux_rand.hex().upper() if aux_rand is not None else None, msg.hex().upper(), sig.hex().upper(), result, comment)
 
-vectors = list(map(lambda vector: bytes_to_hex(vector[0], vector[1], vector[2], vector[3], vector[4], vector[5]), vectors))
+vectors = list(map(lambda vector: bytes_to_hex(vector[0], vector[1], vector[2], vector[3], vector[4], vector[5], vector[6]), vectors))
 
 def print_csv(vectors):
     writer = csv.writer(sys.stdout)
-    writer.writerow(("index", "secret key", "public key", "message", "signature", "verification result", "comment"))
+    writer.writerow(("index", "secret key", "public key", "aux_rand", "message", "signature", "verification result", "comment"))
     for (i,v) in enumerate(vectors):
         writer.writerow((i,)+v)