affine-cipher

Affine Cipher

Create an implementation of the affine cipher, an ancient encryption system created in the Middle East.

The affine cipher is a type of monoalphabetic substitution cipher. Each character is mapped to its numeric equivalent, encrypted with a mathematical function and then converted to the letter relating to its new numeric value. Although all monoalphabetic ciphers are weak, the affine cypher is much stronger than the atbash cipher, because it has many more keys.

the encryption function is:

E(x) = (ax + b) mod m

• where x is the letter's index from 0 - length of alphabet - 1
• m is the length of the alphabet. For the roman alphabet m == 26.
• and a and b make the key

the decryption function is:

D(y) = a^-1(y - b) mod m

• where y is the numeric value of an encrypted letter, ie. y = E(x)
• it is important to note that a^-1 is the modular multiplicative inverse of a mod m
• the modular multiplicative inverse of a only exists if a and m are coprime.

To find the MMI of a:

an mod m = 1

• where n is the modular multiplicative inverse of a mod m

More information regarding how to find a Modular Multiplicative Inverse and what it means can be found here.

Because automatic decryption fails if a is not coprime to m your program should return status 1 and "Error: a and m must be coprime." if they are not. Otherwise it should encode or decode with the provided key.

The Caesar (shift) cipher is a simple affine cipher where a is 1 and b as the magnitude results in a static displacement of the letters. This is much less secure than a full implementation of the affine cipher.

Ciphertext is written out in groups of fixed length, the traditional group size being 5 letters, and punctuation is excluded. This is to make it harder to guess things based on word boundaries.

Examples

• Encoding test gives ybty with the key a=5 b=7
• Decoding ybty gives test with the key a=5 b=7
• Decoding ybty gives lqul with the wrong key a=11 b=7
• Decoding kqlfd jzvgy tpaet icdhm rtwly kqlon ubstx
  • gives thequickbrownfoxjumpsoverthelazydog with the key a=19 b=13
• Encoding test with the key a=18 b=13
  • gives Error: a and m must be coprime.
  • because a and m are not relatively prime

Examples of finding a Modular Multiplicative Inverse (MMI)

• simple example:
  • 9 mod 26 = 9
  • 9 * 3 mod 26 = 27 mod 26 = 1
  • 3 is the MMI of 9 mod 26
• a more complicated example:
  • 15 mod 26 = 15
  • 15 * 7 mod 26 = 105 mod 26 = 1
  • 7 is the MMI of 15 mod 26

Rust Installation

Refer to the exercism help page for Rust installation and learning resources.

Writing the Code

Execute the tests with:

$ cargo test

All but the first test have been ignored. After you get the first test to pass, open the tests source file which is located in the tests directory and remove the #[ignore] flag from the next test and get the tests to pass again. Each separate test is a function with #[test] flag above it. Continue, until you pass every test.

If you wish to run all ignored tests without editing the tests source file, use:

$ cargo test -- --ignored

To run a specific test, for example some_test, you can use:

$ cargo test some_test

If the specific test is ignored use:

$ cargo test some_test -- --ignored

To learn more about Rust tests refer to the online test documentation

Make sure to read the Modules chapter if you haven't already, it will help you with organizing your files.

Further improvements

After you have solved the exercise, please consider using the additional utilities, described in the installation guide, to further refine your final solution.

To format your solution, inside the solution directory use

cargo fmt

To see, if your solution contains some common ineffective use cases, inside the solution directory use

cargo clippy --all-targets

Submitting the solution

Generally you should submit all files in which you implemented your solution (src/lib.rs in most cases). If you are using any external crates, please consider submitting the Cargo.toml file. This will make the review process faster and clearer.

Feedback, Issues, Pull Requests

The exercism/rust repository on GitHub is the home for all of the Rust exercises. If you have feedback about an exercise, or want to help implement new exercises, head over there and create an issue. Members of the rust track team are happy to help!

If you want to know more about Exercism, take a look at the contribution guide.

Source

Wikipedia http://en.wikipedia.org/wiki/Affine_cipher

Submitting Incomplete Solutions

It's possible to submit an incomplete solution so you can see how others have completed the exercise.