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
xis the letter's index from 0 - length of alphabet - 1
mis the length of the alphabet. For the roman alphabet
m == 26.
bmake the key
The decryption function is:
D(y) = a^-1(y - b) mod m
yis the numeric value of an encrypted letter, ie.
y = E(x)
a^-1is the modular multiplicative inverse of
a mod m
aonly exists if
To find the MMI of
an mod m = 1
nis 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
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
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.
ybtywith the key a=5 b=7
testwith the key a=5 b=7
lqulwith the wrong key a=11 b=7
kqlfd jzvgy tpaet icdhm rtwly kqlon ubstx
thequickbrownfoxjumpsoverthelazydogwith the key a=19 b=13
testwith the key a=18 b=13
Error: a and m must be coprime.
9 mod 26 = 9
9 * 3 mod 26 = 27 mod 26 = 1
3is the MMI of
9 mod 26
15 mod 26 = 15
15 * 7 mod 26 = 105 mod 26 = 1
7is the MMI of
15 mod 26
make chez if you're using ChezScheme or
make guile if you're using GNU Guile.
Sometimes the name for the scheme binary on your system will differ from the defaults.
When this is the case, you'll need to tell make by running
make chez chez=your-chez-binary or
make guile guile=your-guile-binary.
(load "test.scm")at the repl prompt.
affine-cipher.scmreloading as you go.
(test)to check your solution.
If some of the test cases fail, you should see the failing input and the expected output.
The failing input is presented as a list because the tests call your solution by
(apply affine-cipher input-list).
To learn more about
apply see The Scheme Programming Language -- Chapter 5