Update test vectors and generation script

3 files changed, 63 insertions, 59 deletions

diff --git a/bip-0340/reference.py b/bip-0340/reference.py
index f24963c..5d17db5 100644
--- a/bip-0340/reference.py
+++ b/bip-0340/reference.py
@@ -66,7 +66,7 @@ def bytes_from_point(P: Point) -> bytes:
 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]:
+def lift_x(b: bytes) -> Optional[Point]:
     x = int_from_bytes(b)
     if x >= p:
         return None
@@ -74,14 +74,7 @@ def lift_x_square_y(b: bytes) -> Optional[Point]:
     y = pow(y_sq, (p + 1) // 4, p)
     if pow(y, 2, p) != y_sq:
         return None
-    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))
+    return (x, y if y & 1 == 0 else p-y)
 
 def int_from_bytes(b: bytes) -> int:
     return int.from_bytes(b, byteorder="big")
@@ -89,15 +82,6 @@ def int_from_bytes(b: bytes) -> int:
 def hash_sha256(b: bytes) -> bytes:
     return hashlib.sha256(b).digest()
 
-def is_square(x: int) -> bool:
-    return int(pow(x, (p - 1) // 2, p)) == 1
-
-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 has_even_y(P: Point) -> bool:
     return y(P) % 2 == 0
 
@@ -120,14 +104,14 @@ def schnorr_sign(msg: bytes, seckey: bytes, aux_rand: bytes) -> bytes:
     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
+    t = xor_bytes(bytes_from_int(d), tagged_hash("BIP0340/aux", aux_rand))
+    k0 = int_from_bytes(tagged_hash("BIP0340/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("BIP340/challenge", bytes_from_point(R) + bytes_from_point(P) + msg)) % n
+    k = n - k0 if not has_even_y(R) else k0
+    e = int_from_bytes(tagged_hash("BIP0340/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):
@@ -141,15 +125,15 @@ def schnorr_verify(msg: bytes, pubkey: bytes, sig: bytes) -> bool:
         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 = lift_x_even_y(pubkey)
+    P = lift_x(pubkey)
     r = int_from_bytes(sig[0:32])
     s = int_from_bytes(sig[32:64])
     if (P is None) or (r >= p) or (s >= n):
         debug_print_vars()
         return False
-    e = int_from_bytes(tagged_hash("BIP340/challenge", sig[0:32] + pubkey + msg)) % n
+    e = int_from_bytes(tagged_hash("BIP0340/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_even_y(R)) or (x(R) != r):
         debug_print_vars()
         return False
     debug_print_vars()
diff --git a/bip-0340/test-vectors.csv b/bip-0340/test-vectors.csv
index beaef5a..a1a63e1 100644
--- a/bip-0340/test-vectors.csv
+++ b/bip-0340/test-vectors.csv
@@ -1,16 +1,16 @@
 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

+0,0000000000000000000000000000000000000000000000000000000000000003,F9308A019258C31049344F85F89D5229B531C845836F99B08601F113BCE036F9,0000000000000000000000000000000000000000000000000000000000000000,0000000000000000000000000000000000000000000000000000000000000000,E907831F80848D1069A5371B402410364BDF1C5F8307B0084C55F1CE2DCA821525F66A4A85EA8B71E482A74F382D2CE5EBEEE8FDB2172F477DF4900D310536C0,TRUE,

+1,B7E151628AED2A6ABF7158809CF4F3C762E7160F38B4DA56A784D9045190CFEF,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,0000000000000000000000000000000000000000000000000000000000000001,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,6896BD60EEAE296DB48A229FF71DFE071BDE413E6D43F917DC8DCF8C78DE33418906D11AC976ABCCB20B091292BFF4EA897EFCB639EA871CFA95F6DE339E4B0A,TRUE,

+2,C90FDAA22168C234C4C6628B80DC1CD129024E088A67CC74020BBEA63B14E5C9,DD308AFEC5777E13121FA72B9CC1B7CC0139715309B086C960E18FD969774EB8,C87AA53824B4D7AE2EB035A2B5BBBCCC080E76CDC6D1692C4B0B62D798E6D906,7E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C,5831AAEED7B44BB74E5EAB94BA9D4294C49BCF2A60728D8B4C200F50DD313C1BAB745879A5AD954A72C45A91C3A51D3C7ADEA98D82F8481E0E1E03674A6F3FB7,TRUE,

+3,0B432B2677937381AEF05BB02A66ECD012773062CF3FA2549E44F58ED2401710,25D1DFF95105F5253C4022F628A996AD3A0D95FBF21D468A1B33F8C160D8F517,FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF,FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF,7EB0509757E246F19449885651611CB965ECC1A187DD51B64FDA1EDC9637D5EC97582B9CB13DB3933705B32BA982AF5AF25FD78881EBB32771FC5922EFC66EA3,TRUE,test fails if msg is reduced modulo p or n

+4,,D69C3509BB99E412E68B0FE8544E72837DFA30746D8BE2AA65975F29D22DC7B9,,4DF3C3F68FCC83B27E9D42C90431A72499F17875C81A599B566C9889B9696703,00000000000000000000003B78CE563F89A0ED9414F5AA28AD0D96D6795F9C6376AFB1548AF603B3EB45C9F8207DEE1060CB71C04E80F593060B07D28308D7F4,TRUE,

+5,,EEFDEA4CDB677750A420FEE807EACF21EB9898AE79B9768766E4FAA04A2D4A34,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,6CFF5C3BA86C69EA4B7376F31A9BCB4F74C1976089B2D9963DA2E5543E17776969E89B4C5564D00349106B8497785DD7D1D713A8AE82B32FA79D5F7FC407D39B,FALSE,public key not on the curve

+6,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,FFF97BD5755EEEA420453A14355235D382F6472F8568A18B2F057A14602975563CC27944640AC607CD107AE10923D9EF7A73C643E166BE5EBEAFA34B1AC553E2,FALSE,has_even_y(R) is false

+7,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,1FA62E331EDBC21C394792D2AB1100A7B432B013DF3F6FF4F99FCB33E0E1515F28890B3EDB6E7189B630448B515CE4F8622A954CFE545735AAEA5134FCCDB2BD,FALSE,negated message

+8,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,6CFF5C3BA86C69EA4B7376F31A9BCB4F74C1976089B2D9963DA2E5543E177769961764B3AA9B2FFCB6EF947B6887A226E8D7C93E00C5ED0C1834FF0D0C2E6DA6,FALSE,negated s value

+9,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,0000000000000000000000000000000000000000000000000000000000000000123DDA8328AF9C23A94C1FEECFD123BA4FB73476F0D594DCB65C6425BD186051,FALSE,sG - eP is infinite. Test fails in single verification if has_even_y(inf) is defined as true and x(inf) as 0

+10,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,00000000000000000000000000000000000000000000000000000000000000017615FBAF5AE28864013C099742DEADB4DBA87F11AC6754F93780D5A1837CF197,FALSE,sG - eP is infinite. Test fails in single verification if has_even_y(inf) is defined as true and x(inf) as 1

+11,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,4A298DACAE57395A15D0795DDBFD1DCB564DA82B0F269BC70A74F8220429BA1D69E89B4C5564D00349106B8497785DD7D1D713A8AE82B32FA79D5F7FC407D39B,FALSE,sig[0:32] is not an X coordinate on the curve

+12,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F69E89B4C5564D00349106B8497785DD7D1D713A8AE82B32FA79D5F7FC407D39B,FALSE,sig[0:32] is equal to field size

+13,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,6CFF5C3BA86C69EA4B7376F31A9BCB4F74C1976089B2D9963DA2E5543E177769FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141,FALSE,sig[32:64] is equal to curve order

+14,,FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC30,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,6CFF5C3BA86C69EA4B7376F31A9BCB4F74C1976089B2D9963DA2E5543E17776969E89B4C5564D00349106B8497785DD7D1D713A8AE82B32FA79D5F7FC407D39B,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 9c029ec..e5b8847 100644
--- a/bip-0340/test-vectors.py
+++ b/bip-0340/test-vectors.py
@@ -1,6 +1,14 @@
 import sys
 from reference import *
 
+def is_square(x):
+    return int(pow(x, (p - 1) // 2, p)) == 1
+
+def has_square_y(P):
+    """Determine if P has a square Y coordinate. Used in an earlier draft of BIP340."""
+    assert not is_infinity(P)
+    return is_square(P[1])
+
 def vector0():
     seckey = bytes_from_int(3)
     msg = bytes_from_int(0)
@@ -19,9 +27,16 @@ def vector0():
     # 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)
+    pubkey_point = lift_x(pubkey)
     assert(not has_square_y(pubkey_point))
 
+    # For historical reasons (R tiebreaker was squareness and not evenness)
+    # we should have at least one test vector where the the point reconstructed
+    # from the R.x coordinate has a square and one where it has a non-square Y
+    # coordinate. In this one Y is non-square.
+    R = lift_x(sig[0:32])
+    assert(not has_square_y(R))
+
     return (seckey, pubkey, aux_rand, msg, sig, "TRUE", None)
 
 def vector1():
@@ -30,6 +45,11 @@ def vector1():
     aux_rand = bytes_from_int(1)
 
     sig = schnorr_sign(msg, seckey, aux_rand)
+
+    # The point reconstructed from the R.x coordinate has a square Y coordinate.
+    R = lift_x(sig[0:32])
+    assert(has_square_y(R))
+
     return (seckey, pubkey_gen(seckey), aux_rand, msg, sig, "TRUE", None)
 
 def vector2():
@@ -40,13 +60,13 @@ def vector2():
 
     # The point reconstructed from the public key has a square Y coordinate.
     pubkey = pubkey_gen(seckey)
-    pubkey_point = lift_x_even_y(pubkey)
+    pubkey_point = lift_x(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 = lift_x_square_y(sig[0:32])
-    assert(not is_square(R[0]))
+    # evenness of the X coordinate of R instead of the Y coordinate.
+    R = lift_x(sig[0:32])
+    assert(R[0] % 2 == 1)
 
     return (seckey, pubkey, aux_rand, msg, sig, "TRUE", None)
 
@@ -66,7 +86,7 @@ def vector3():
 
 # 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
-# square.
+# even.
 def insecure_schnorr_sign_fixed_nonce(msg, seckey0, k):
     if len(msg) != 32:
         raise ValueError('The message must be a 32-byte array.')
@@ -76,12 +96,12 @@ def insecure_schnorr_sign_fixed_nonce(msg, seckey0, k):
     P = point_mul(G, seckey0)
     seckey = seckey0 if has_even_y(P) else n - seckey0
     R = point_mul(G, k)
-    e = int_from_bytes(tagged_hash("BIP340/challenge", bytes_from_point(R) + bytes_from_point(P) + msg)) % n
+    e = int_from_bytes(tagged_hash("BIP0340/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
+# Creates a singature with a small x(R) by using k = -1/2
 def vector4():
-    one_half = 0x7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b20a0
+    one_half = n - 0x7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b20a0
     seckey = bytes_from_int(0x763758E5CBEEDEE4F7D3FC86F531C36578933228998226672F13C4F0EBE855EB)
     msg = bytes_from_int(0x4DF3C3F68FCC83B27E9D42C90431A72499F17875C81A599B566C9889B9696703)
     sig = insecure_schnorr_sign_fixed_nonce(msg, seckey, one_half)
@@ -100,21 +120,21 @@ def vector5():
     sig = schnorr_sign(msg, seckey, default_aux_rand)
 
     pubkey = bytes_from_int(0xEEFDEA4CDB677750A420FEE807EACF21EB9898AE79B9768766E4FAA04A2D4A34)
-    assert(lift_x_even_y(pubkey) is None)
+    assert(lift_x(pubkey) is None)
 
     return (None, pubkey, None, msg, sig, "FALSE", "public key not on the curve")
 
 def vector6():
     seckey = default_seckey
     msg = default_msg
-    k = 3
+    k = 6
     sig = insecure_schnorr_sign_fixed_nonce(msg, seckey, k)
 
-    # Y coordinate of R is not a square
+    # Y coordinate of R is not even
     R = point_mul(G, k)
-    assert(not has_square_y(R))
+    assert(not has_even_y(R))
 
-    return (None, pubkey_gen(seckey), None, msg, sig, "FALSE", "has_square_y(R) is false")
+    return (None, pubkey_gen(seckey), None, msg, sig, "FALSE", "has_even_y(R) is false")
 
 def vector7():
     seckey = default_seckey
@@ -147,7 +167,7 @@ def vector9():
     sig = insecure_schnorr_sign_fixed_nonce(msg, seckey, k)
     bytes_from_point.__code__ = bytes_from_point_tmp
 
-    return (None, pubkey_gen(seckey), 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")
+    return (None, pubkey_gen(seckey), None, msg, sig, "FALSE", "sG - eP is infinite. Test fails in single verification if has_even_y(inf) is defined as true and x(inf) as 0")
 
 def bytes_from_point_inf1(P):
     if P == None:
@@ -166,7 +186,7 @@ def vector10():
     sig = insecure_schnorr_sign_fixed_nonce(msg, seckey, k)
     bytes_from_point.__code__ = bytes_from_point_tmp
 
-    return (None, pubkey_gen(seckey), 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")
+    return (None, pubkey_gen(seckey), None, msg, sig, "FALSE", "sG - eP is infinite. Test fails in single verification if has_even_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
@@ -178,7 +198,7 @@ def vector11():
 
     # Replace R's X coordinate with an X coordinate that's not on the curve
     x_not_on_curve = bytes_from_int(0x4A298DACAE57395A15D0795DDBFD1DCB564DA82B0F269BC70A74F8220429BA1D)
-    assert(lift_x_square_y(x_not_on_curve) is None)
+    assert(lift_x(x_not_on_curve) is None)
     sig = x_not_on_curve + sig[32:64]
 
     return (None, pubkey_gen(seckey), None, msg, sig, "FALSE", "sig[0:32] is not an X coordinate on the curve")
@@ -222,10 +242,10 @@ def vector14():
     sig = schnorr_sign(msg, seckey, default_aux_rand)
     pubkey_int = p + 1
     pubkey = bytes_from_int(pubkey_int)
-    assert(lift_x_even_y(pubkey) is None)
+    assert(lift_x(pubkey) is None)
     # If an implementation would reduce a given public key modulo p then the
     # pubkey would be valid
-    assert(lift_x_even_y(bytes_from_int(pubkey_int % p)) is not None)
+    assert(lift_x(bytes_from_int(pubkey_int % p)) is not None)
 
     return (None, pubkey, None, msg, sig, "FALSE", "public key is not a valid X coordinate because it exceeds the field size")