Rename BIPs

bip-0340/reference.py

@@ -0,0 +1,169 @@
+import hashlib
+import binascii
+
+p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F
+n = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141
+
+# Points are tuples of X and Y coordinates and the point at infinity is
+# represented by the None keyword.
+G = (0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798, 0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8)
+
+# 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):
+    tag_hash = hashlib.sha256(tag.encode()).digest()
+    return hashlib.sha256(tag_hash + tag_hash + msg).digest()
+
+def is_infinity(P):
+    return P is None
+
+def x(P):
+    return P[0]
+
+def y(P):
+    return P[1]
+
+def point_add(P1, P2):
+    if (P1 is None):
+        return P2
+    if (P2 is None):
+        return P1
+    if (x(P1) == x(P2) and y(P1) != y(P2)):
+        return None
+    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):
+    R = None
+    for i in range(256):
+        if ((n >> i) & 1):
+            R = point_add(R, P)
+        P = point_add(P, P)
+    return R
+
+def bytes_from_int(x):
+    return x.to_bytes(32, byteorder="big")
+
+def bytes_from_point(P):
+    return bytes_from_int(x(P))
+
+def point_from_bytes(b):
+    x = int_from_bytes(b)
+    if x >= p:
+        return None
+    y_sq = (pow(x, 3, p) + 7) % p
+    y = pow(y_sq, (p + 1) // 4, p)
+    if pow(y, 2, p) != y_sq:
+        return None
+    return [x, y]
+
+def int_from_bytes(b):
+    return int.from_bytes(b, byteorder="big")
+
+def hash_sha256(b):
+    return hashlib.sha256(b).digest()
+
+def is_square(x):
+    return pow(x, (p - 1) // 2, p) == 1
+
+def has_square_y(P):
+    return not is_infinity(P) and is_square(y(P))
+
+def pubkey_gen(seckey):
+    x = int_from_bytes(seckey)
+    if not (1 <= x <= n - 1):
+        raise ValueError('The secret key must be an integer in the range 1..n-1.')
+    P = point_mul(G, x)
+    return bytes_from_point(P)
+
+def schnorr_sign(msg, seckey0):
+    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):
+        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 k0 == 0:
+        raise RuntimeError('Failure. This happens only with negligible probability.')
+    R = point_mul(G, k0)
+    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):
+    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
+    r = int_from_bytes(sig[0:32])
+    s = int_from_bytes(sig[32:64])
+    if (r >= p or s >= n):
+        return False
+    e = int_from_bytes(tagged_hash("BIPSchnorr", 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:
+        return False
+    return True
+
+#
+# The following code is only used to verify the test vectors.
+#
+import csv
+
+def test_vectors():
+    all_passed = True
+    with open('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)
+                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())
+                    all_passed = False
+            result_actual = schnorr_verify(msg, pubkey, sig)
+            if result == result_actual:
+                print(' * Passed verification test.')
+            else:
+                print(' * Failed verification test.')
+                print('   Expected verification result:', result)
+                print('     Actual verification result:', result_actual)
+                if comment:
+                    print('   Comment:', comment)
+                all_passed = False
+    print()
+    if all_passed:
+        print('All test vectors passed.')
+    else:
+        print('Some test vectors failed.')
+    return all_passed
+
+if __name__ == '__main__':
+    test_vectors()

bip-0340/test-vectors.csv

@@ -0,0 +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

bip-0340/test-vectors.py

@@ -0,0 +1,241 @@
+import sys
+from reference import *
+
+def vector0():
+    seckey = bytes_from_int(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 (seckey, pubkey, 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)
+
+    return (seckey, pubkey, msg, sig, "TRUE", None)
+
+def vector2():
+    seckey = bytes_from_int(0xC90FDAA22168C234C4C6628B80DC1CD129024E088A67CC74020BBEA63B14E5C9)
+    msg = bytes_from_int(0x5E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C)
+    sig = schnorr_sign(msg, seckey)
+
+    # 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])
+    assert(not is_square(R[0]))
+
+    return (seckey, pubkey_gen(seckey), msg, sig, "TRUE", None)
+
+def vector3():
+    seckey = bytes_from_int(0x0B432B2677937381AEF05BB02A66ECD012773062CF3FA2549E44F58ED2401710)
+    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")
+
+# 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.
+def insecure_schnorr_sign_fixed_nonce(msg, seckey0, k):
+    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):
+        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
+    R = point_mul(G, k)
+    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)
+
+# Creates a singature with a small x(R) by using k = 1/2
+def vector4():
+    one_half = 0x7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b20a0
+    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)
+
+default_seckey = bytes_from_int(0xB7E151628AED2A6ABF7158809CF4F3C762E7160F38B4DA56A784D9045190CFEF)
+default_msg = bytes_from_int(0x243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89)
+
+# Public key is not on the curve
+def vector5():
+    # This creates a dummy signature that doesn't have anything to do with the
+    # public key.
+    seckey = default_seckey
+    msg = default_msg
+    sig = schnorr_sign(msg, seckey)
+
+    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 = insecure_schnorr_sign_fixed_nonce(msg, seckey, k)
+
+    # Y coordinate of R is not a square
+    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")
+
+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 = 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")
+
+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 = 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")
+
+# 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")
+
+# Test out of range pubkey
+# It's cryptographically impossible to create a test vector that fails if run
+# in an implementation which accepts out of range pubkeys because we can't find
+# a secret key for such a public key and therefore can not create a signature.
+# This test vector just increases test coverage.
+def vector14():
+    # This creates a dummy signature that doesn't have anything to do with the
+    # public key.
+    seckey = default_seckey
+    msg = default_msg
+    sig = schnorr_sign(msg, seckey)
+
+    pubkey_int = p + 1
+    pubkey = bytes_from_int(pubkey_int)
+    assert(point_from_bytes(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)
+
+    return (None, pubkey, msg, sig, "FALSE", "public key is not a valid X coordinate because it exceeds the field size")
+
+vectors = [
+        vector0(),
+        vector1(),
+        vector2(),
+        vector3(),
+        vector4(),
+        vector5(),
+        vector6(),
+        vector7(),
+        vector8(),
+        vector9(),
+        vector10(),
+        vector11(),
+        vector12(),
+        vector13(),
+        vector14()
+    ]
+
+# 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)