Switch to 32 byte public keys in bip-schnorr

bip-schnorr/reference.py

@@ -31,19 +31,14 @@ def bytes_from_int(x):
     return x.to_bytes(32, byteorder="big")
 
 def bytes_from_point(P):
-    return (b'\x03' if P[1] & 1 else b'\x02') + bytes_from_int(P[0])
+    return bytes_from_int(P[0])
 
 def point_from_bytes(b):
-    if b[0:1] in [b'\x02', b'\x03']:
-        odd = b[0] - 0x02
-    else:
-        return None
-    x = int_from_bytes(b[1:33])
+    x = int_from_bytes(b)
     y_sq = (pow(x, 3, p) + 7) % p
-    y0 = pow(y_sq, (p + 1) // 4, p)
-    if pow(y0, 2, p) != y_sq:
+    y = pow(y_sq, (p + 1) // 4, p)
+    if pow(y, 2, p) != y_sq:
         return None
-    y = p - y0 if y0 & 1 != odd else y0
     return [x, y]
 
 def int_from_bytes(b):
@@ -55,24 +50,30 @@ def hash_sha256(b):
 def jacobi(x):
     return pow(x, (p - 1) // 2, p)
 
-def schnorr_sign(msg, seckey):
+def pubkey_gen(seckey):
+    P = point_mul(G, seckey)
+    return bytes_from_point(P)
+
+def schnorr_sign(msg, seckey0):
     if len(msg) != 32:
         raise ValueError('The message must be a 32-byte array.')
-    if not (1 <= seckey <= n - 1):
+    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 (jacobi(P[1]) == 1) else n - seckey0
     k0 = int_from_bytes(hash_sha256(bytes_from_int(seckey) + msg)) % n
     if k0 == 0:
         raise RuntimeError('Failure. This happens only with negligible probability.')
     R = point_mul(G, k0)
     k = n - k0 if (jacobi(R[1]) != 1) else k0
-    e = int_from_bytes(hash_sha256(bytes_from_int(R[0]) + bytes_from_point(point_mul(G, seckey)) + msg)) % n
-    return bytes_from_int(R[0]) + bytes_from_int((k + e * seckey) % n)
+    e = int_from_bytes(hash_sha256(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):
     if len(msg) != 32:
         raise ValueError('The message must be a 32-byte array.')
-    if len(pubkey) != 33:
-        raise ValueError('The public key must be a 33-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)
@@ -82,7 +83,7 @@ def schnorr_verify(msg, pubkey, sig):
     s = int_from_bytes(sig[32:64])
     if (r >= p or s >= n):
         return False
-    e = int_from_bytes(hash_sha256(sig[0:32] + bytes_from_point(P) + msg)) % n
+    e = int_from_bytes(hash_sha256(sig[0:32] + pubkey + msg)) % n
     R = point_add(point_mul(G, s), point_mul(P, n - e))
     if R is None or jacobi(R[1]) != 1 or R[0] != r:
         return False
@@ -107,20 +108,25 @@ def test_vectors():
             print('\nTest vector #%-3i: ' % int(index))
             if seckey != '':
                 seckey = int(seckey, 16)
+                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('   Excepted signature:', sig.hex())
-                    print('     Actual signature:', sig_actual.hex())
+                    print('   Expected signature:', sig.hex().upper())
+                    print('     Actual signature:', sig_actual.hex().upper())
                     all_passed = False
             result_actual = schnorr_verify(msg, pubkey, sig)
             if result == result_actual:
                 print(' * Passed verification test.')
             else:
                 print(' * Failed verification test.')
-                print('   Excepted verification result:', result)
+                print('   Expected verification result:', result)
                 print('     Actual verification result:', result_actual)
                 if comment:
                     print('   Comment:', comment)

bip-schnorr/test-vectors.csv

@@ -1,17 +1,15 @@
 index,secret key,public key,message,signature,verification result,comment
-1,0000000000000000000000000000000000000000000000000000000000000001,0279BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798,0000000000000000000000000000000000000000000000000000000000000000,787A848E71043D280C50470E8E1532B2DD5D20EE912A45DBDD2BD1DFBF187EF67031A98831859DC34DFFEEDDA86831842CCD0079E1F92AF177F7F22CC1DCED05,TRUE,
-2,B7E151628AED2A6ABF7158809CF4F3C762E7160F38B4DA56A784D9045190CFEF,02DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,2A298DACAE57395A15D0795DDBFD1DCB564DA82B0F269BC70A74F8220429BA1D1E51A22CCEC35599B8F266912281F8365FFC2D035A230434A1A64DC59F7013FD,TRUE,
-3,C90FDAA22168C234C4C6628B80DC1CD129024E088A67CC74020BBEA63B14E5C7,03FAC2114C2FBB091527EB7C64ECB11F8021CB45E8E7809D3C0938E4B8C0E5F84B,5E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C,00DA9B08172A9B6F0466A2DEFD817F2D7AB437E0D253CB5395A963866B3574BE00880371D01766935B92D2AB4CD5C8A2A5837EC57FED7660773A05F0DE142380,TRUE,
-4,,03DEFDEA4CDB677750A420FEE807EACF21EB9898AE79B9768766E4FAA04A2D4A34,4DF3C3F68FCC83B27E9D42C90431A72499F17875C81A599B566C9889B9696703,00000000000000000000003B78CE563F89A0ED9414F5AA28AD0D96D6795F9C6302A8DC32E64E86A333F20EF56EAC9BA30B7246D6D25E22ADB8C6BE1AEB08D49D,TRUE,
-5,,031B84C5567B126440995D3ED5AABA0565D71E1834604819FF9C17F5E9D5DD078F,0000000000000000000000000000000000000000000000000000000000000000,52818579ACA59767E3291D91B76B637BEF062083284992F2D95F564CA6CB4E3530B1DA849C8E8304ADC0CFE870660334B3CFC18E825EF1DB34CFAE3DFC5D8187,TRUE,"test fails if jacobi symbol of x(R) instead of y(R) is used"
-6,,03FAC2114C2FBB091527EB7C64ECB11F8021CB45E8E7809D3C0938E4B8C0E5F84B,FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF,570DD4CA83D4E6317B8EE6BAE83467A1BF419D0767122DE409394414B05080DCE9EE5F237CBD108EABAE1E37759AE47F8E4203DA3532EB28DB860F33D62D49BD,TRUE,"test fails if msg is reduced modulo p or n"
-7,,03EEFDEA4CDB677750A420FEE807EACF21EB9898AE79B9768766E4FAA04A2D4A34,4DF3C3F68FCC83B27E9D42C90431A72499F17875C81A599B566C9889B9696703,00000000000000000000003B78CE563F89A0ED9414F5AA28AD0D96D6795F9C6302A8DC32E64E86A333F20EF56EAC9BA30B7246D6D25E22ADB8C6BE1AEB08D49D,FALSE,"public key not on the curve"
-8,,02DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,2A298DACAE57395A15D0795DDBFD1DCB564DA82B0F269BC70A74F8220429BA1DFA16AEE06609280A19B67A24E1977E4697712B5FD2943914ECD5F730901B4AB7,FALSE,"incorrect R residuosity"
-9,,03FAC2114C2FBB091527EB7C64ECB11F8021CB45E8E7809D3C0938E4B8C0E5F84B,5E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C, 00DA9B08172A9B6F0466A2DEFD817F2D7AB437E0D253CB5395A963866B3574BED092F9D860F1776A1F7412AD8A1EB50DACCC222BC8C0E26B2056DF2F273EFDEC,FALSE,"negated message"
-10,,0279BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798,0000000000000000000000000000000000000000000000000000000000000000,787A848E71043D280C50470E8E1532B2DD5D20EE912A45DBDD2BD1DFBF187EF68FCE5677CE7A623CB20011225797CE7A8DE1DC6CCD4F754A47DA6C600E59543C,FALSE,"negated s value"
-11,,03DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,2A298DACAE57395A15D0795DDBFD1DCB564DA82B0F269BC70A74F8220429BA1D1E51A22CCEC35599B8F266912281F8365FFC2D035A230434A1A64DC59F7013FD,FALSE,"negated public key"
-12,,02DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,00000000000000000000000000000000000000000000000000000000000000009E9D01AF988B5CEDCE47221BFA9B222721F3FA408915444A4B489021DB55775F,FALSE,"sG - eP is infinite. Test fails in single verification if jacobi(y(inf)) is defined as 1 and x(inf) as 0"
-13,,02DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,0000000000000000000000000000000000000000000000000000000000000001D37DDF0254351836D84B1BD6A795FD5D523048F298C4214D187FE4892947F728,FALSE,"sG - eP is infinite. Test fails in single verification if jacobi(y(inf)) is defined as 1 and x(inf) as 1"
-14,,02DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,4A298DACAE57395A15D0795DDBFD1DCB564DA82B0F269BC70A74F8220429BA1D1E51A22CCEC35599B8F266912281F8365FFC2D035A230434A1A64DC59F7013FD,FALSE,"sig[0:32] is not an X coordinate on the curve"
-15,,02DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC2F1E51A22CCEC35599B8F266912281F8365FFC2D035A230434A1A64DC59F7013FD,FALSE,"sig[0:32] is equal to field size"
-16,,02DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,2A298DACAE57395A15D0795DDBFD1DCB564DA82B0F269BC70A74F8220429BA1DFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141,FALSE,"sig[32:64] is equal to curve order"
+0,0000000000000000000000000000000000000000000000000000000000000001,79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798,0000000000000000000000000000000000000000000000000000000000000000,787A848E71043D280C50470E8E1532B2DD5D20EE912A45DBDD2BD1DFBF187EF6166FCCEE14F021B31AF22A90D0639CC010C2B764C304A8FFF266ABBC01A0A880,TRUE,
+1,B7E151628AED2A6ABF7158809CF4F3C762E7160F38B4DA56A784D9045190CFEF,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,3C4D3ADB1F05C3E948216ECB6007D1534D97D35D5589EDB226AD0370C0293C780AEA9BA361509DA2FDF7BC6E5E38926E40B6ACCD24EA9E06B9DA8244A1D0B691,TRUE,
+2,C90FDAA22168C234C4C6628B80DC1CD129024E088A67CC74020BBEA63B14E5C7,FAC2114C2FBB091527EB7C64ECB11F8021CB45E8E7809D3C0938E4B8C0E5F84B,5E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C,33380A613013115518CD6030ABC8220B2DED273FD3ABD13DF0882DC6A928E5AFAC72DF3248F8FAC522EF1A819EE5EE5BEA81D92D0E19A6FAB228E5D1D61BF833,TRUE,
+3,0B432B2677937381AEF05BB02A66ECD012773062CF3FA2549E44F58ED2401710,25D1DFF95105F5253C4022F628A996AD3A0D95FBF21D468A1B33F8C160D8F517,FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF,7C4E8B0C2575A77A01AF41EE6678EF9C41F97CC4D15FF6D6CA45D73BC6FF7FF4919D246589AF2FA6306F4B7A392857E9C4A17CB21DBE72C38A48C99979EEDCB8,TRUE,test fails if msg is reduced modulo p or n
+4,,D69C3509BB99E412E68B0FE8544E72837DFA30746D8BE2AA65975F29D22DC7B9,4DF3C3F68FCC83B27E9D42C90431A72499F17875C81A599B566C9889B9696703,00000000000000000000003B78CE563F89A0ED9414F5AA28AD0D96D6795F9C63F84A709CFFD89AD94FCBD808D41BD26BF62F263AA253527134DDC4A4715BF491,TRUE,
+5,,EEFDEA4CDB677750A420FEE807EACF21EB9898AE79B9768766E4FAA04A2D4A34,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,3C4D3ADB1F05C3E948216ECB6007D1534D97D35D5589EDB226AD0370C0293C780AEA9BA361509DA2FDF7BC6E5E38926E40B6ACCD24EA9E06B9DA8244A1D0B691,FALSE,public key not on the curve
+6,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,F9308A019258C31049344F85F89D5229B531C845836F99B08601F113BCE036F98631F4EF21D5F231A1000ED069E0348ED057EDF4FB1B6672009EDE9DBB2DEE14,FALSE,incorrect R residuosity
+7,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,07636CBE3092D11AFCA4DD1D32E50F039EB5FF5FB2AB72A7DC2BA0F3A4E7ED418C312ED6ABF6A41446D28789DF4AA43A15E166F001D072536ADC6E49C21DC419,FALSE,negated message
+8,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,3C4D3ADB1F05C3E948216ECB6007D1534D97D35D5589EDB226AD0370C0293C78F515645C9EAF625D02084391A1C76D9079F830198A5E023505F7DC482E658AB0,FALSE,negated s value
+9,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,0000000000000000000000000000000000000000000000000000000000000000221A96FEEBA7AD29F11B675DB394948A83A220FD8FE181A7667BDBEE178011B1,FALSE,sG - eP is infinite. Test fails in single verification if jacobi(y(inf)) is defined as 1 and x(inf) as 0
+10,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,00000000000000000000000000000000000000000000000000000000000000011A39648F31350D8E591106B43B9EB364F8617BCD52DC96A3FA8C4E50347F31DE,FALSE,sG - eP is infinite. Test fails in single verification if jacobi(y(inf)) is defined as 1 and x(inf) as 1
+11,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,4A298DACAE57395A15D0795DDBFD1DCB564DA82B0F269BC70A74F8220429BA1D0AEA9BA361509DA2FDF7BC6E5E38926E40B6ACCD24EA9E06B9DA8244A1D0B691,FALSE,sig[0:32] is not an X coordinate on the curve
+12,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F0AEA9BA361509DA2FDF7BC6E5E38926E40B6ACCD24EA9E06B9DA8244A1D0B691,FALSE,sig[0:32] is equal to field size
+13,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,3C4D3ADB1F05C3E948216ECB6007D1534D97D35D5589EDB226AD0370C0293C78FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141,FALSE,sig[32:64] is equal to curve order

bip-schnorr/test-vectors.py

@@ -0,0 +1,215 @@
+import sys
+from reference import *
+
+def vector0():
+    seckey = 1
+    msg = bytes_from_int(0)
+    sig = schnorr_sign(msg, seckey)
+    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)
+
+    return (bytes_from_int(seckey), pubkey, msg, sig, "TRUE", None)
+
+def vector1():
+    seckey = 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)
+
+    return (bytes_from_int(seckey), pubkey, msg, sig, "TRUE", None)
+
+def vector2():
+    seckey = 0xC90FDAA22168C234C4C6628B80DC1CD129024E088A67CC74020BBEA63B14E5C7
+    msg = bytes_from_int(0x5E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C)
+    sig = schnorr_sign(msg, seckey)
+
+    # This signature does not verify vector if the implementer would check the
+    # jacobi symbol of the X coordinate of R instead of the Y coordinate.
+    R = point_from_bytes(sig[0:32])
+    assert(jacobi(R[0]) != 1)
+
+    return (bytes_from_int(seckey), pubkey_gen(seckey), msg, sig, "TRUE", None)
+
+def vector3():
+    seckey = 0x0B432B2677937381AEF05BB02A66ECD012773062CF3FA2549E44F58ED2401710
+    msg = bytes_from_int(0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)
+    sig = schnorr_sign(msg, seckey)
+    return (bytes_from_int(seckey), pubkey_gen(seckey), msg, sig, "TRUE", "test fails if msg is reduced modulo p or n")
+
+# Signs with a given nonce. Results in an invalid signature if y(kG) is not a
+# quadratic residue.
+def schnorr_sign_fixed_nonce(msg, seckey0, k):
+    if len(msg) != 32:
+        raise ValueError('The message must be a 32-byte array.')
+    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 (jacobi(P[1]) == 1) else n - seckey0
+    R = point_mul(G, k)
+    e = int_from_bytes(hash_sha256(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
+def vector4():
+    one_half = 0x7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b20a0
+    seckey = 0x763758E5CBEEDEE4F7D3FC86F531C36578933228998226672F13C4F0EBE855EB
+    msg = bytes_from_int(0x4DF3C3F68FCC83B27E9D42C90431A72499F17875C81A599B566C9889B9696703)
+    sig = schnorr_sign_fixed_nonce(msg, seckey, one_half)
+    return (None, pubkey_gen(seckey), msg, sig, "TRUE", None)
+
+default_seckey = 0xB7E151628AED2A6ABF7158809CF4F3C762E7160F38B4DA56A784D9045190CFEF
+default_msg = bytes_from_int(0x243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89)
+
+def vector5():
+    seckey = default_seckey
+    msg = default_msg
+    sig = schnorr_sign(msg, seckey)
+
+    # Public key is not on the curve
+    pubkey = bytes_from_int(0xEEFDEA4CDB677750A420FEE807EACF21EB9898AE79B9768766E4FAA04A2D4A34)
+    assert(point_from_bytes(pubkey) is None)
+
+    return (None, pubkey, msg, sig, "FALSE", "public key not on the curve")
+
+def vector6():
+    seckey = default_seckey
+    msg = default_msg
+    k = 3
+    sig = schnorr_sign_fixed_nonce(msg, seckey, k)
+
+    # Y coordinate of R is not a quadratic residue
+    R = point_mul(G, k)
+    assert(jacobi(R[1]) != 1)
+
+    return (None, pubkey_gen(seckey), msg, sig, "FALSE", "incorrect R residuosity")
+
+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")
+
+def vector8():
+    seckey = default_seckey
+    msg = default_msg
+    sig = schnorr_sign(msg, seckey)
+    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")
+
+def bytes_from_point_inf0(P):
+    if P == None:
+        return bytes_from_int(0)
+    return bytes_from_int(P[0])
+
+def vector9():
+    seckey = default_seckey
+    msg = default_msg
+
+    # Override bytes_from_point in schnorr_sign to allow creating a signature
+    # with k = 0.
+    k = 0
+    bytes_from_point_tmp = bytes_from_point.__code__
+    bytes_from_point.__code__ = bytes_from_point_inf0.__code__
+    sig = 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 jacobi(y(inf)) is defined as 1 and x(inf) as 0")
+
+def bytes_from_point_inf1(P):
+    if P == None:
+        return bytes_from_int(1)
+    return bytes_from_int(P[0])
+
+def vector10():
+    seckey = default_seckey
+    msg = default_msg
+
+    # Override bytes_from_point in schnorr_sign to allow creating a signature
+    # with k = 0.
+    k = 0
+    bytes_from_point_tmp = bytes_from_point.__code__
+    bytes_from_point.__code__ = bytes_from_point_inf1.__code__
+    sig = 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 jacobi(y(inf)) is defined as 1 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
+# coordinate on the curve. This test vector just increases test coverage.
+def vector11():
+    seckey = default_seckey
+    msg = default_msg
+    sig = schnorr_sign(msg, seckey)
+
+    # 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)
+    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")
+
+# 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
+# than the field size. This test vector just increases test coverage.
+def vector12():
+    seckey = default_seckey
+    msg = default_msg
+    sig = schnorr_sign(msg, seckey)
+
+    # 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")
+
+# 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
+# than the curve order. This test vector just increases test coverage.
+def vector13():
+    seckey = default_seckey
+    msg = default_msg
+    sig = schnorr_sign(msg, seckey)
+
+    # 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")
+
+vectors = [
+        vector0(),
+        vector1(),
+        vector2(),
+        vector3(),
+        vector4(),
+        vector5(),
+        vector6(),
+        vector7(),
+        vector8(),
+        vector9(),
+        vector10(),
+        vector11(),
+        vector12(),
+        vector13(),
+    ]
+
+# 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)
+
+vectors = list(map(lambda vector: bytes_to_hex(vector[0], vector[1], vector[2], vector[3], vector[4], vector[5]), vectors))
+
+def print_csv(vectors):
+    writer = csv.writer(sys.stdout)
+    writer.writerow(("index", "secret key", "public key", "message", "signature", "verification result", "comment"))
+    for (i,v) in enumerate(vectors):
+        writer.writerow((i,)+v)
+
+print_csv(vectors)