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:

constpolynomial=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