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.gitignore
vendored
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184
.gitignore
vendored
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@ -0,0 +1,184 @@
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# Created by .ignore support plugin (hsz.mobi)
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### Python template
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# Byte-compiled / optimized / DLL files
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__pycache__/
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*.py[cod]
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*$py.class
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# C extensions
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*.so
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# Distribution / packaging
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.Python
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env/
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develop-eggs/
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dist/
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downloads/
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lib64/
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var/
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*.egg-info/
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.installed.cfg
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*.egg
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# PyInstaller
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# Usually these files are written by a python script from a template
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# before PyInstaller builds the exe, so as to inject date/other infos into it.
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*.manifest
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# Installer logs
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coverage.xml
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*,cover
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# Translations
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*.mo
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# Django stuff:
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*.log
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instance/
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.scrapy
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celerybeat-schedule
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ENV/
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# Spyder project settings
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.spyderproject
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### VirtualEnv template
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# Virtualenv
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# http://iamzed.com/2009/05/07/a-primer-on-virtualenv/
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[Bb]in
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[Ii]nclude
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[Ll]ib
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[Ll]ib64
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[Ll]ocal
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[Ss]cripts
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pyvenv.cfg
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### JetBrains template
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# Covers JetBrains IDEs: IntelliJ, RubyMine, PhpStorm, AppCode, PyCharm, CLion, Android Studio, WebStorm and Rider
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# Reference: https://intellij-support.jetbrains.com/hc/en-us/articles/206544839
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# Gradle
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# When using Gradle or Maven with auto-import, you should exclude module files,
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# since they will be recreated, and may cause churn. Uncomment if using
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cmake-build-*/
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out/
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# idea folder, uncomment if you don't need it
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.idea
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262
lib/gcd_tables.py
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262
lib/gcd_tables.py
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'''
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Source: extendedeuclideanalgorithm.com
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Modified to generate CSV tables
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for iterative calculation of the modular inverse
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'''
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import math
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# Warning: can't handle b=0. See extendedeuclideanalgorithm.com/code for a version that can
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def gcd_iterative(a, b):
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""" Calculating the greatest common divisor
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using the Euclidean Algorithm (non-recursive)
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(Source: extendedeuclideanalgorithm.com/code)
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"""
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# Set default values for the quotient and the remainder
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q = 0
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r = 1
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'''
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In each iteration of the loop below, we
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calculate the new quotient, remainder, a and b.
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r decreases, so we stop when r = 0
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'''
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while (r > 0):
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# The calculations
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q = math.floor(a / b)
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r = a - q * b
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# The values for the next iteration
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a = b
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b = r if (r > 0) else b
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return abs(b)
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# Can handle b=0
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def gcd_iterative_2(a, b):
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""" Calculating the greatest common divisor
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using the Euclidean Algorithm (non-recursive)
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(Source: extendedeuclideanalgorithm.com/code)
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"""
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# Set default values for the quotient and the remainder
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q = 0
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r = 1
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'''
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In each iteration of the loop below, we
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calculate the new quotient, remainder, a and b.
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r decreases, so we stop when r = 0
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'''
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while (b > 0):
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# The calculations
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q = math.floor(a / b)
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r = a - q * b
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# The values for the next iteration
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a = b
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b = r
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return abs(a)
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def gcd(a, b):
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""" Calculating the greatest common divisor
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using the Euclidean Algorithm (recursive)
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(Source: extendedeuclideanalgorithm.com/code)
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"""
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if (b == 0):
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return abs(a)
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q = math.floor(a / b)
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r = a - q * b
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return abs(b) if (r == 0) else gcd(b, r)
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# Warning: this version can't handle b=0. See extendedeuclideanalgorithm.com/code for a version that can.
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def xgcd_iterative(a, b):
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""" Calculates the gcd and Bezout coefficients,
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using the Extended Euclidean Algorithm (non-recursive).
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(Source: extendedeuclideanalgorithm.com/code)
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"""
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# Set default values for the quotient, remainder,
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# s-variables and t-variables
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q = 0
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r = 1
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s1 = 1
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s2 = 0
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s3 = 1
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t1 = 0
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t2 = 1
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t3 = 0
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'''
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In each iteration of the loop below, we
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calculate the new quotient, remainder, a, b,
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and the new s-variables and t-variables.
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r decreases, so we stop when r = 0
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'''
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while (r > 0):
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# The calculations
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q = math.floor(a / b)
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r = a - q * b
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s3 = s1 - q * s2
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t3 = t1 - q * t2
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'''
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The values for the next iteration,
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(but only if there is a next iteration)
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'''
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if (r > 0):
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a = b
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b = r
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s1 = s2
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s2 = s3
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t1 = t2
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t2 = t3
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return abs(b), s2, t2
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# Can handle b=0
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def xgcd_iterative_2(a, b):
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""" Calculates the gcd and Bezout coefficients,
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using the Extended Euclidean Algorithm (non-recursive).
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(Source: extendedeuclideanalgorithm.com/code)
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"""
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# Set default values for the quotient, remainder,
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# s-variables and t-variables
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q = 0
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r = 1
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s1 = 1
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s2 = 0
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s3 = 1
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t1 = 0
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t2 = 1
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t3 = 0
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'''
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In each iteration of the loop below, we
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calculate the new quotient, remainder, a, b,
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and the new s-variables and t-variables.
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r decreases, so we stop when r = 0
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'''
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# CSV output
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print("i, n, b, q, r, t1, t2, t3")
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i = 1
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while (b > 0):
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# The calculations
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q = math.floor(a / b)
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r = a - q * b
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s3 = s1 - q * s2
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t3 = t1 - q * t2
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# CSV output
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print("{}, {}, {}, {}, {}, {}, {}, {}".format(i, a, b, q, r, t1, t2, t3))
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i += 1
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'''
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The values for the next iteration,
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(but only if there is a next iteration)
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'''
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a = b
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b = r
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s1 = s2
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s2 = s3
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t1 = t2
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t2 = t3
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return abs(a), s1, t1
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def xgcd(a, b, s1=1, s2=0, t1=0, t2=1):
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""" Calculates the gcd and Bezout coefficients,
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using the Extended Euclidean Algorithm (recursive).
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(Source: extendedeuclideanalgorithm.com/code)
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"""
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if (b == 0):
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return abs(a), 1, 0
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q = math.floor(a / b)
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r = a - q * b
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s3 = s1 - q * s2
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t3 = t1 - q * t2
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# if r==0, then b will be the gcd and s2, t2 the Bezout coefficients
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return (abs(b), s2, t2) if (r == 0) else xgcd(b, r, s2, s3, t2, t3)
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def multinv(b, n):
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"""
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Calculates the multiplicative inverse of a number b mod n,
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using the Extended Euclidean Algorithm. If b does not have a
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multiplicative inverse mod n, then throw an exception.
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(Source: extendedeuclideanalgorithm.com/code)
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"""
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# Get the gcd and the second Bezout coefficient (t)
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# from the Extended Euclidean Algorithm. (We don't need s)
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my_gcd, _, t = xgcd(n, b)
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# It only has a multiplicative inverse if the gcd is 1
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if (my_gcd == 1):
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return t % n
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else:
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raise ValueError('{} has no multiplicative inverse modulo {}'.format(b, n))
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def make_eea_table(a : int, b : int):
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'''
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Euclidean algorithm:
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see the output of gcd(a, b)
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'''
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print('Euclidean Algorithm:')
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print('The gcd of', a, 'and', b, 'is', gcd(a, b))
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# -------------------------------------------------------------
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'''
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Extended Euclidean Algorithm:
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see the output of xgcd(a,b) and Bezout coefficients
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And verify that they are correct
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'''
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my_gcd, s, t = xgcd(a, b)
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verification = abs(s * a + t * b)
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print('Extended Euclidean Algorithm:')
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print('The gcd of', a, 'and', b, 'is', my_gcd)
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print('And the Bezout coefficients: s=', s, ' and t=', t, '.', sep='')
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print('And', s, '*', a, '+', t, '*', b, '=', verification)
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if (my_gcd == verification):
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print('So as we expect, s*a+t*b is equal to the gcd we found.')
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else:
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print('Something went wrong')
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# ------------------------------------------------------------
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b = b
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n = a
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'''
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Multiplicative Inverse:
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Try to compute the multiplicative inverse of b mod n.
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If that succeeds, verify that it's correct.
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If it doesn't succeed, show the error raised by the function.
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'''
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print('Multiplicative inverse:')
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try:
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# inverse = multinv(b, n);
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inverse = xgcd_iterative_2(b, n)
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except ValueError as error:
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print(error)
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|
10
make_eea_takes.py
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10
make_eea_takes.py
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@ -0,0 +1,10 @@
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from lib.gcd_tables import *
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def check():
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make_eea_table(7, 143)
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# Press the green button in the gutter to run the script.
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if __name__ == '__main__':
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check()
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60
shanks_baby_giant_step.py
Normal file
60
shanks_baby_giant_step.py
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from math import ceil, sqrt
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def bsgs(p, g, h):
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##Berechne d in h = g^d mod p
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N = ceil(sqrt(p - 1)) # phi(p) is p-1 if p is prime
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# Baby step: compute a look-up table of g^i values for i = 0, 1, ..., N
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lookup_table = {pow(g, i, p): i for i in range(N)}
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# Precompute via Fermat's Little Theorem
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c = pow(g, N * (p - 2), p)
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# Giant step: Search for an equivalence in the lookup_table
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for j in range(N):
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y = (h * pow(c, j, p)) % p
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if y in lookup_table:
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return j * N + lookup_table[y]
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# Solution not found
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return None
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|
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|
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def main():
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p = 27893
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g = 3729
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alpha = 11819
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beta = 1531
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# Find the discrete logarithm a such that g^a = alpha mod p
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a = bsgs(p, g, alpha)
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print(f"a = {a}")
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# Validate the result
|
||||
if a is None:
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print("No solution found for a")
|
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else:
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# Recompute the shared secret key: K = beta^a mod p
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K = pow(beta, a, p)
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print(f"Shared secret key K = {K}")
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# Find the discrete logarithm b such that g^b = beta mod p
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b = bsgs(p, g, beta)
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print(f"b = {b}")
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# Validate the result
|
||||
if b is None:
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print("No solution found for b")
|
||||
else:
|
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# Recompute the shared secret key: K = alpha^b mod p
|
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K2 = pow(alpha, b, p)
|
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if K2 == K:
|
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print("b is correct")
|
||||
else:
|
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print("b is not correct")
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
main()
|
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