jupyter.txt

import ecc
import helper

from ecc import FieldElement, Point
---
exercise1:
prime = 223
a = FieldElement(0, prime)
b = FieldElement(7, prime)

# (192,105), (17,56), (200,119), (1,193), (42,99)
---
example1
---
example3
---
exercise2:
prime = 223
a = FieldElement(0, prime)
b = FieldElement(7, prime)

# (170,142) + (60,139)
# (47,71) + (17,56)
# (143,98) + (76,66)
---
exercise3:ecc:ECCTest:test_add
---
exercise4:
prime = 223
a = FieldElement(0, prime)
b = FieldElement(7, prime)

# 2*(192, 105)
# 2*(143, 98)
# 2*(47, 71)
# 4*(47, 71)
# 8*(47, 71)
# 21*(47, 71)

# create a product variable
# add the point to the product n times
# print the product
---
example4
---
exercise5:
prime = 223
a = FieldElement(0, prime)
b = FieldElement(7, prime)
x = FieldElement(15, prime)
y = FieldElement(86, prime)
p = Point(x, y, a, b)
inf = Point(None, None, a, b)

# create a product variable
# create a counter variable
# loop until the product is the point at infinity
# add the point to the product and increment counter
# print the counter when exited from loop
---
example5
---
example6
---
example7
---
example8
---
example9
---
exercise6:
point = S256Point(
    0x887387e452b8eacc4acfde10d9aaf7f6d9a0f975aabb10d006e4da568744d06c, 
    0x61de6d95231cd89026e286df3b6ae4a894a3378e393e93a0f45b666329a0ae34)
# signature 1
z = 0xec208baa0fc1c19f708a9ca96fdeff3ac3f230bb4a7ba4aede4942ad003c0f60
r = 0xac8d1c87e51d0d441be8b3dd5b05c8795b48875dffe00b7ffcfac23010d3a395
s = 0x68342ceff8935ededd102dd876ffd6ba72d6a427a3edb13d26eb0781cb423c4
# signature 2
z = 0x7c076ff316692a3d7eb3c3bb0f8b1488cf72e1afcd929e29307032997a838a3d
r = 0xeff69ef2b1bd93a66ed5219add4fb51e11a840f404876325a1e8ffe0529a2c
s = 0xc7207fee197d27c618aea621406f6bf5ef6fca38681d82b2f06fddbdce6feab6
---
example10
---
exercise7:
# Exercise 7

e = 12345
z = int.from_bytes(hash256(b'Programming Bitcoin!'), 'big')

# choose a random k
# calculate r (kG's x-coordinate)
# calculate s ((z+re)/k)
# print the point, z, r and s