├── README.md
├── RSA Python.sln
├── RSA Python.pyproj
└── RSA_Python.py


/README.md:
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 1 | # RSA-Python
 2 | The RSA algorithm coded in Python
 3 | 
 4 | Created in collaboration with [Unnikrishnan Menon](https://github.com/7enTropy7)
 5 | 
 6 | **RSA Algorithm**
 7 | * Pick two large primes $p,q$.
 8 | * Compute $n=pq$ and $\varphi(n)=\mathrm{lcm}(p-1,q-1)$
 9 | * Choose a public key $e$ such that $1< e< \varphi(n)$ and $\gcd(e,\varphi(n))=1$
10 | * Calculate $d$ such that $de\equiv 1 \pmod\varphi(n)$
11 | * Let the message **key** be $m$
12 | * **Encrypt: ** $c\equiv m^e\pmod n$
13 | * **Decrypt: ** $m\equiv c^d\pmod n$
14 | 
15 | ![image](https://user-images.githubusercontent.com/7680591/59566357-3a722d00-902d-11e9-991c-b67e5f369722.png)
16 | 
17 | And this is what a code says….
18 | ![rsa](https://user-images.githubusercontent.com/7680591/59566011-0e07e200-9028-11e9-9f54-449d0ff23a28.jpg)
19 | 
20 | Note that you may have to setup an external dependency environment in some cases, it would create a big chunk of files that are not here due to exceeding the maximum number of files to upload.
21 | 


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/RSA Python.sln:
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 1 | 
 2 | Microsoft Visual Studio Solution File, Format Version 12.00
 3 | # Visual Studio Version 16
 4 | VisualStudioVersion = 16.0.29009.5
 5 | MinimumVisualStudioVersion = 10.0.40219.1
 6 | Project("{888888A0-9F3D-457C-B088-3A5042F75D52}") = "RSA Python", "RSA Python.pyproj", "{24393137-B8A3-41AD-B263-39AAB3586B47}"
 7 | EndProject
 8 | Global
 9 | 	GlobalSection(SolutionConfigurationPlatforms) = preSolution
10 | 		Debug|Any CPU = Debug|Any CPU
11 | 		Release|Any CPU = Release|Any CPU
12 | 	EndGlobalSection
13 | 	GlobalSection(ProjectConfigurationPlatforms) = postSolution
14 | 		{24393137-B8A3-41AD-B263-39AAB3586B47}.Debug|Any CPU.ActiveCfg = Debug|Any CPU
15 | 		{24393137-B8A3-41AD-B263-39AAB3586B47}.Release|Any CPU.ActiveCfg = Release|Any CPU
16 | 	EndGlobalSection
17 | 	GlobalSection(SolutionProperties) = preSolution
18 | 		HideSolutionNode = FALSE
19 | 	EndGlobalSection
20 | 	GlobalSection(ExtensibilityGlobals) = postSolution
21 | 		SolutionGuid = {80DC23D8-68E3-4C6C-9A9B-629315FE5E4F}
22 | 	EndGlobalSection
23 | EndGlobal
24 | 


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/RSA Python.pyproj:
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 1 | <Project DefaultTargets="Build" xmlns="http://schemas.microsoft.com/developer/msbuild/2003" ToolsVersion="4.0">
 2 |   <PropertyGroup>
 3 |     <Configuration Condition=" '$(Configuration)' == '' ">Debug</Configuration>
 4 |     <SchemaVersion>2.0</SchemaVersion>
 5 |     <ProjectGuid>24393137-b8a3-41ad-b263-39aab3586b47</ProjectGuid>
 6 |     <ProjectHome>.</ProjectHome>
 7 |     <StartupFile>RSA_Python.py</StartupFile>
 8 |     <SearchPath>
 9 |     </SearchPath>
10 |     <WorkingDirectory>.</WorkingDirectory>
11 |     <OutputPath>.</OutputPath>
12 |     <Name>RSA Python</Name>
13 |     <RootNamespace>RSA Python</RootNamespace>
14 |     <InterpreterId>MSBuild|env|$(MSBuildProjectFullPath)</InterpreterId>
15 |   </PropertyGroup>
16 |   <PropertyGroup Condition=" '$(Configuration)' == 'Debug' ">
17 |     <DebugSymbols>true</DebugSymbols>
18 |     <EnableUnmanagedDebugging>false</EnableUnmanagedDebugging>
19 |   </PropertyGroup>
20 |   <PropertyGroup Condition=" '$(Configuration)' == 'Release' ">
21 |     <DebugSymbols>true</DebugSymbols>
22 |     <EnableUnmanagedDebugging>false</EnableUnmanagedDebugging>
23 |   </PropertyGroup>
24 |   <ItemGroup>
25 |     <Compile Include="RSA_Python.py" />
26 |   </ItemGroup>
27 |   <ItemGroup>
28 |     <Interpreter Include="env\">
29 |       <Id>env</Id>
30 |       <Version>3.7</Version>
31 |       <Description>env (Python 3.7 (32-bit))</Description>
32 |       <InterpreterPath>Scripts\python.exe</InterpreterPath>
33 |       <WindowsInterpreterPath>Scripts\pythonw.exe</WindowsInterpreterPath>
34 |       <PathEnvironmentVariable>PYTHONPATH</PathEnvironmentVariable>
35 |       <Architecture>X86</Architecture>
36 |     </Interpreter>
37 |   </ItemGroup>
38 |   <Import Project="$(MSBuildExtensionsPath32)\Microsoft\VisualStudio\v$(VisualStudioVersion)\Python Tools\Microsoft.PythonTools.targets" />
39 |   <!-- Uncomment the CoreCompile target to enable the Build command in
40 |        Visual Studio and specify your pre- and post-build commands in
41 |        the BeforeBuild and AfterBuild targets below. -->
42 |   <!--<Target Name="CoreCompile" />-->
43 |   <Target Name="BeforeBuild">
44 |   </Target>
45 |   <Target Name="AfterBuild">
46 |   </Target>
47 | </Project>


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/RSA_Python.py:
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  1 | from math import sqrt
  2 | #required for the sqrt() function, if you want to avoid doing **0.5
  3 | import random
  4 | #required for randrange
  5 | from random import randint as rand
  6 | 
  7 | #just to use the well known keyword rand() from C++
  8 | 
  9 | 
 10 | def gcd(a, b):
 11 |     if b == 0:
 12 |         return a
 13 |     else:
 14 |         return gcd(b, a % b)
 15 | 
 16 | 
 17 | def mod_inverse(a, m):
 18 |     for x in range(1, m):
 19 |         if (a * x) % m == 1:
 20 |             return x
 21 |     return -1
 22 | 
 23 | 
 24 | def isprime(n):
 25 |     if n < 2:
 26 |         return False
 27 |     elif n == 2:
 28 |         return True
 29 |     else:
 30 |         for i in range(2, int(sqrt(n)) + 1, 2):
 31 |             if n % i == 0:
 32 |                 return False
 33 |     return True
 34 | 
 35 | 
 36 | #initial two random numbers p,q
 37 | p = rand(1, 1000)
 38 | q = rand(1, 1000)
 39 | 
 40 | 
 41 | def generate_keypair(p, q, keysize):
 42 |     # keysize is the bit length of n so it must be in range(nMin,nMax+1).
 43 |     # << is bitwise operator
 44 |     # x << y is same as multiplying x by 2**y
 45 |     # i am doing this so that p and q values have similar bit-length.
 46 |     # this will generate an n value that's hard to factorize into p and q.
 47 | 
 48 |     nMin = 1 << (keysize - 1)
 49 |     nMax = (1 << keysize) - 1
 50 |     primes = [2]
 51 |     # we choose two prime numbers in range(start, stop) so that the difference of bit lengths is at most 2.
 52 |     start = 1 << (keysize // 2 - 1)
 53 |     stop = 1 << (keysize // 2 + 1)
 54 | 
 55 |     if start >= stop:
 56 |         return []
 57 | 
 58 |     for i in range(3, stop + 1, 2):
 59 |         for p in primes:
 60 |             if i % p == 0:
 61 |                 break
 62 |         else:
 63 |             primes.append(i)
 64 | 
 65 |     while (primes and primes[0] < start):
 66 |         del primes[0]
 67 | 
 68 |     #choosing p and q from the generated prime numbers.
 69 |     while primes:
 70 |         p = random.choice(primes)
 71 |         primes.remove(p)
 72 |         q_values = [q for q in primes if nMin <= p * q <= nMax]
 73 |         if q_values:
 74 |             q = random.choice(q_values)
 75 |             break
 76 |     print(p, q)
 77 |     n = p * q
 78 |     phi = (p - 1) * (q - 1)
 79 | 
 80 |     #generate public key 1<e<phi(n)
 81 |     e = random.randrange(1, phi)
 82 |     g = gcd(e, phi)
 83 | 
 84 |     while True:
 85 |         #as long as gcd(1,phi(n)) is not 1, keep generating e
 86 |         e = random.randrange(1, phi)
 87 |         g = gcd(e, phi)
 88 |         #generate private key
 89 |         d = mod_inverse(e, phi)
 90 |         if g == 1 and e != d:
 91 |             break
 92 | 
 93 |     #public key (e,n)
 94 |     #private key (d,n)
 95 | 
 96 |     return ((e, n), (d, n))
 97 | 
 98 | 
 99 | def encrypt(msg_plaintext, package):
100 |     #unpack key value pair
101 |     e, n = package
102 |     msg_ciphertext = [pow(ord(c), e, n) for c in msg_plaintext]
103 |     return msg_ciphertext
104 | 
105 | 
106 | def decrypt(msg_ciphertext, package):
107 |     d, n = package
108 |     msg_plaintext = [chr(pow(c, d, n)) for c in msg_ciphertext]
109 |     # No need to use ord() since c is now a number
110 |     # After decryption, we cast it back to character
111 |     # to be joined in a string for the final result
112 |     return (''.join(msg_plaintext))
113 | 
114 | 
115 | #-------------------------------------------------------------
116 | #driver program
117 | if __name__ == "__main__":
118 |     bit_length = int(input("Enter bit_length: "))
119 |     print("Running RSA...")
120 |     print("Generating public/private keypair...")
121 |     public, private = generate_keypair(
122 |         p, q, 2**bit_length)  # 8 is the keysize (bit-length) value.
123 |     print("Public Key: ", public)
124 |     print("Private Key: ", private)
125 |     msg = input("Write msg: ")
126 |     print([ord(c) for c in msg])
127 |     encrypted_msg = encrypt(msg, public)
128 |     print("Encrypted msg: ")
129 |     print(''.join(map(lambda x: str(x), encrypted_msg)))
130 |     print("Decrypted msg: ")
131 |     print(decrypt(encrypted_msg, private))
132 | 


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