RegressionCipher

A cipher that uses regression to encrypt a word

How it works?

Encoding

First, let's take a small string (this cipher doesn't handle long string):

"Hello World!"

Then, we take its Unicode Scalars representation in an array:

{
    "0": 72,
    "1": 101,
    "2": 108,
    "3": 108,
    "4": 111,
    "5": 32,
    "6": 87,
    "7": 111,
    "8": 114,
    "9": 108,
    "10": 100,
    "11": 33
}

We place these points on a graph, and we're trying to find a polynomial function that passes through these points. This is called a polynomial regression. By default, we're looking for a 50 degree polynomial, this mean that we're looking for a function with x^50 in it.

This is the most difficult part of this cipher. On the js implementation, we use TheoremJS to help us finding this curve.

That's what the graph looks like: This is an absolute mess!

When we have our function, we take the polynomial's constants and we put them in an array:

[7.460811086912491e-46,-7.962405118584728e-45,1.9278177172115392e-45,-3.5498651021822254e-42,1.5186448672981877e-41,-4.121622223200062e-41,4.04820982223833e-39,-1.8738877919982897e-38,-4.086439268485582e-38,-2.178663346321919e-37,-1.2163569091919228e-35,4.403761801345783e-34,-1.892292543888421e-33,-1.9247541585132566e-32,8.550561303064075e-32,-1.663472057615308e-30,-3.399209092513209e-29,1.1955863899190084e-27,4.967073699309138e-27,7.525767895574489e-26,-1.4721968061815467e-24,-2.2247371855035983e-24,-1.26356074868432e-22,5.868551264524077e-22,2.022664462484692e-20,9.632814297363559e-20,-2.1413071158603019e-19,-1.1255807521972845e-17,-2.9799892953240315e-16,6.508087352915873e-16,-2.5785604873749457e-14,4.057695624368721e-13,-3.493535338048475e-12,3.764475288666697e-11,-2.6778776484082267e-10,3.0675833766998695e-9,1.8468211834686325e-8,-1.777489976431793e-7,0.00000316330304168273,-0.000055624507062443935,-0.00017749393967649563,0.0005029266193315753,0.048850204878434784,-0.024854249421857127,-3.7587677945914724,21.32517859935154,-35.06355640424047,-20.192777609490225,87.04041721662499,-20.3736200267882,71.99981834159912]

And we return the base64 representation of this array:
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Decoding

We take the text above, and we decode it using base64. We parse this array, and we create a polynomial from this array:

const polynomial = t.polynomial(...constants) // t is referring to TheoremJS, and constants to the array above

Implementations

Language	Encrypt	Decrypt
Javascript	encrypt.js	decrypt.js
Javascript (no dependencies)	encrypt-v2.js	decrypt-v2.js

Running the tests

Tests are automatically handled by Travis CI.

Contributing

Please read CONTRIBUTING.md for details on our code of conduct, and the process for submitting pull requests to us.

Versioning

We use SemVer for versioning. For the versions available, see the tags on this repository.

Authors

Arthur Guiot - Initial work & conception - @arguiot

See also the list of contributors who participated in this project.

License

This project is licensed under the MIT License - see the

file for details

CrypTools / RegressionCipher