rsasim

A pure python implementation of rsa, for fun and experimenting. Please note that to be used in production a lot of constraints have to be imposed on rsa and that the given module only serves as a proof of concept and should not be used in production.

Demo

• RSA Blinding attack using the rsasim module

Installation

$ git clone https://github.com/kaushiksk/rsasim && cd rsasim

$ pip install . --user

or

$ python setup.py install --user

For python3 install, run the second command with pip3 or the last command with python3.

Components

In addition to the rsasim package, two command line scripts isprime and genprime are also installed.

Usage

rsasim

>>> from rsasim import RSA
>>> A = RSA()  # Alice
>>> B = RSA()  # Bob
>>> E = RSA()  # Eve

Alice wants to talk to Bob so she will encrypt her message using Bob's public key

>>> ciphertext_B = A.encrypt("Hello Bob", B.public_key)
>>> B.decrypt(ciphertext_B) 
'Hello Bob'

If Eve tries to decrypt this

>>> E.decrypt(ciphertext_B)
'\x12\x0eA\x8c\xc5\x1f\xa1\x05\xfe\x80Q\x1e\x1b|\xbb\xb8\xe9\xa6\x84\xc1\xda\x8b:XC\xed\x91\xb8\x12q\x11\xd9'

The above result may vary as the keys are randomly generated each time.

The API remains the same for numbers

>>> ciphertext_E = A.encrypt(123456789, E.public_key)
>>> E.decrypt(ciphertext_E)
123456789L
>>> B.decrypt(ciphertext_E)
4081228201739686282145927510867027940582326297585236661320804597753581131993L

You can view anyone's public key but cannot alter it directly.

>>> A.public_key = (2,3)
Exception: You are not allowed to alter generated keys
>> A.public_key
(56618467399119298776135038168667997056624964942029346840873882494861567586229L, 92020774583088837673591629484044516416427751099585188055672485398962861161269L)

Digital signatures can be achieved in a similar manner. Alice signs a string or number with her private key.

>>> sign_a = A.sign("Alice's Signature")

Bob or Eve can verify this. It can only be verified with Alice's public key.

>>> B.verify(sign_a, A.public_key)
"Alice's Signature"
>>> E.verify(sign_a, A.public_key)
"Alice's Signature"
>>> B.verify(sign_a, E.public_key)
'\x1cv\x04@j\xf2\x04\x83!\xab\x01uN\xd8\x02Y\xc8\xd43\rD\x59c9I@c\x92\x0c)/\xe2\x9c0'

The process_string() and recover_string() @classmethods are used to convert between byte strings and long integers. It is a slightly simplified version of the code here

>>> RSA.process_string("Hi Bob")
79616349990754
>> RSA.process_string("Hi Bob what's up?")
24640066858828187311071388516817835487295L
>>> RSA.recover_string(79616349990754)
'Hi Bob'

isprime

Check whether a number is prime or not from the command line. The script internally uses the Miller Rabin Primality test.

$ isprime 13
True
$ isprime 213
False

genprime

Generate a random prime number. A 100 bit random prime number is generated by default. You can generate a fixed bit length prime using the --bits argument.

$ genprime
213209838925001955916657635071
$ genprime --bits 50
419883489883873
$ genprime -h

Development Notes

For development notes and commit history check this repo