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import random
import sys
p = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f
n = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
E = EllipticCurve(GF(p), [0, 7])
G = E.point( (0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798,0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8)) # Base point
def egcd(a, b):
if a == 0:
return (b, 0, 1)
else:
g, y, x = egcd(b % a, a)
return (g, x - (b // a) * y, y)
def modinv(a, m):
g, x, y = egcd(a, m)
if g != 1:
raise Exception('modular inverse does not exist')
else:
return x % m
def verify(r, s,z,public_key):
w = int(modinv(s, n))
u1 = int((z * w) % n)
u2 = int((r * w) % n)
D=u1*G + u2*public_key
x,y=D.xy()
x=int(x)
if (r % n) == (x % n):
print( "signature matches")
return 1
else:
print("invalid signature",r,x%n,hex(int(x%n)))
return -1
def decom(e):
e_arr = []
for i in range(256):
e_arr.append(e % 2**1)
e = e >> 1
e_arr.reverse()
return e_arr
def create_table(t):
# input : t -> length of tables ( from 1 to max. 255 this values it depends of bits message hash) - chosed by an user
# output: table_i_0 and table_i_1 -> randomised Points
table_i_0={}
table_i_1={}
for i in range(0,t):
a1=random.randrange(1,n)
a2=random.randrange(1,n)
table_i_0[i]=(G*a1,a1)
table_i_1[i]=(G*a2,a2)
return table_i_0,table_i_1
def make_r_of_hash(hash_values,tableG_0,tableG_1,t):
#Algo:
#round-based scalar multiplication
# decomposite message hash to bits as [0 1 0 1 1 1 0 1 ....]
decomp_hash=decom(hash_values)
#Input :the bits(e1,e2,...,e256) of the hash_value (little-endian order) as decomp_hash
#Output: r-coordinate of [k]*G and the message- dependent scalar k
#Start
# Round 1: input e1, k1,0 ,k1,1, G1,0, G1,1 embedded values
# where e1 -> decomp_hash[0]
# where G1,0 -> tableG_0
# where G1,12 -> tableG_1
# R ←[1−e1]*G1,0 + [e1]*G1,12
# k ←(1−e1)*k1,0 + e1 * k1,12
# Generate nonce for sign of transaction using two tables and bits of message hash
e1=decomp_hash[0]
#Round 1
G10,k10=tableG_0[0]
G11,k11=tableG_1[0]
R=(1-e1)*G10+e1*G11
k=((1-e1)*k10+e1*k11)%n
#Round 2:
# input(R,k,ei),ki,0,ki,1,Gi,0,Gi,1 embedded values
# for 2≤ i≤ t do :
# R← R+ [1−ei]*Gi,0+ [ei]*Gi,1
# k←k+ (1−ei)*ki,0+ei*ki,1
# return Rx,k
for i in range(1,t):
Gi0,k1i=tableG_0[i]
G1i,ki1=tableG_1[i]
ei= decomp_hash[i]
R=R+(1-ei)*Gi0+ei*G1i
k=(k+(1-ei)*k1i+ei*ki1)%n
return R,k
def sign_transaction(privkey,message,rounds):
z=message
tableG_i_0,tableG_i_1=create_table(rounds)
R,nonce=make_r_of_hash(z,tableG_i_0,tableG_i_1,rounds)
r=R.xy()[0]
r=int(r)
s=(z+int(r)*privkey)*modinv(nonce,n)%n
return int(r), int(s), int(z),nonce
pr=100
message= random.randrange(1,n)
rounds=10
r,s,z,nonce=sign_transaction(pr,message,rounds)
verify(r,s,z,pr*G)
print("trans #1")
print("nonce=",nonce)
print("r=",r)
print("s=",s)
print("z=",z)
pr=100
rounds=10
r,s,z,nonce=sign_transaction(pr,message,rounds)
verify(r,s,z,pr*G)
print()
print("trans #2")
print("nonce=",nonce)
print("r=",r)
print("s=",s)
print("z=",z)
import random
import sys
p = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f
n = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
E = EllipticCurve(GF(p), [0, 7])
G = E.point( (0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798,0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8)) # Base point
def egcd(a, b):
if a == 0:
return (b, 0, 1)
else:
g, y, x = egcd(b % a, a)
return (g, x - (b // a) * y, y)
def modinv(a, m):
g, x, y = egcd(a, m)
if g != 1:
raise Exception('modular inverse does not exist')
else:
return x % m
def verify(r, s,z,public_key):
w = int(modinv(s, n))
u1 = int((z * w) % n)
u2 = int((r * w) % n)
D=u1*G + u2*public_key
x,y=D.xy()
x=int(x)
if (r % n) == (x % n):
print( "signature matches")
return 1
else:
print("invalid signature",r,x%n,hex(int(x%n)))
return -1
def decom(e):
e_arr = []
for i in range(256):
e_arr.append(e % 2**1)
e = e >> 1
e_arr.reverse()
return e_arr
def create_table(t):
table_i_0={}
table_i_1={}
for i in range(0,t):
a1=random.randrange(1,n)
a2=random.randrange(1,n)
table_i_0[i]=(G*a1,a1)
table_i_1[i]=(G*a2,a2)
return table_i_0,table_i_1
def make_r_of_hash(hash_values,tableG_0,tableG_1,t):
decomp_hash=decom(hash_values)
e1=decomp_hash[0]
#Round 1
G10,k10=tableG_0[0]
G11,k11=tableG_1[0]
#Round 2
R=(1-e1)*G10+e1*G11
k=((1-e1)*k10+e1*k11)%n
for i in range(1,t):
Gi0,k1i=tableG_0[i]
G1i,ki1=tableG_1[i]
ei= decomp_hash[i]
R=R+(1-ei)*Gi0+ei*G1i
k=(k+(1-ei)*k1i+ei*ki1)%n
return R,k
def sign_transaction(privkey,message,rounds):
z=message
tableG_i_0,tableG_i_1=create_table(rounds)
R,nonce=make_r_of_hash(z,tableG_i_0,tableG_i_1,rounds)
r=R.xy()[0]
r=int(r)
s=(z+int(r)*privkey)*modinv(nonce,n)%n
return int(r), int(s), int(z),nonce
pr=100
message= random.randrange(1,n)
rounds=10
r,s,z,nonce=sign_transaction(pr,message,rounds)
verify(r,s,z,pr*G)
print("trans #1")
print("nonce=",nonce)
print("r=",r)
print("s=",s)
print("z=",z)
pr=100
message= random.randrange(1,n)
rounds=4
r,s,z,nonce=sign_transaction(pr,message,rounds)
verify(r,s,z,pr*G)
print()
print("trans #2")
print("nonce=",nonce)
print("r=",r)
print("s=",s)
print("z=",z)
e_arr.append(e % 2**1)
import random
import sys
p = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f
n = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
E = EllipticCurve(GF(p), [0, 7])
G = E.point( (0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798,0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8)) # Base point
def egcd(a, b):
if a == 0:
return (b, 0, 1)
else:
g, y, x = egcd(b % a, a)
return (g, x - (b // a) * y, y)
def modinv(a, m):
g, x, y = egcd(a, m)
if g != 1:
raise Exception('modular inverse does not exist')
else:
return x % m
def verify(r, s,z,public_key):
w = int(modinv(s, n))
u1 = int((z * w) % n)
u2 = int((r * w) % n)
D=u1*G + u2*public_key
x,y=D.xy()
x=int(x)
if (r % n) == (x % n):
print( "signature matches")
return 1
else:
print("invalid signature",r,x%n,hex(int(x%n)))
return -1
def decom(e):
e_arr = []
for i in range(256):
e_arr.append(e % 2**1)
e = e >> 1
e_arr.reverse()
return e_arr
def create_table(t):
table_i_0={}
table_i_1={}
for i in range(0,t):
a1=random.randrange(1,n)
a2=random.randrange(1,n)
table_i_0[i]=(G*a1,a1)
table_i_1[i]=(G*a2,a2)
return table_i_0,table_i_1
def make_r_of_hash(hash_values,tableG_0,tableG_1,t):
decomp_hash=decom(hash_values)
e1=decomp_hash[0]
#Round 1
G10,k10=tableG_0[0]
G11,k11=tableG_1[0]
#Round 2
R=(1-e1)*G10+e1*G11
k=((1-e1)*k10+e1*k11)%n
for i in range(1,t):
Gi0,k1i=tableG_0[i]
G1i,ki1=tableG_1[i]
ei= decomp_hash[i]
R=R+(1-ei)*Gi0+ei*G1i
k=(k+(1-ei)*k1i+ei*ki1)%n
return R,k
def sign_transaction(privkey,message,rounds):
z=message
tableG_i_0,tableG_i_1=create_table(rounds)
R,nonce=make_r_of_hash(z,tableG_i_0,tableG_i_1,rounds)
r=R.xy()[0]
r=int(r)
s=(z+int(r)*privkey)*modinv(nonce,n)%n
return int(r), int(s), int(z),nonce
pr=100
message= random.randrange(1,n)
rounds=10
r,s,z,nonce=sign_transaction(pr,message,rounds)
verify(r,s,z,pr*G)
print("trans #1")
print("nonce=",nonce)
print("r=",r)
print("s=",s)
print("z=",z)
pr=100
message= random.randrange(1,n)
rounds=4
r,s,z,nonce=sign_transaction(pr,message,rounds)
verify(r,s,z,pr*G)
print()
print("trans #2")
print("nonce=",nonce)
print("r=",r)
print("s=",s)
print("z=",z)