# Mystika

The Mystika project seeks to deliver an industrial quality, high-performance cryptographic library with forward-looking features and very high-level code. The idea is to deliver a cryptographic foundation for critical software that consists of a small, efficient, and easy to audit code base built on very high-level coding practices. Here are some key goals:

• Demonstrably Reliable
• Safe and future-worthy cryptography only
• Protocol level compatibility with existing standards when possible
• Easy to use

Dictionary

Here are the verbs, nouns, adverbs, and conjunctions provided by this project.

Data Structures

BA ⍝ Bignum Array
PA ⍝ Bigpoly Array
bf ⍝ Bignum function
NBA ⍝ Nested bignum Array

A bignum array is an array where the 0th axis is used for the places of a number in a given base, and the first 3 elements of that axis are reserved for metadata. The metadata has the following format:

• the 0th element specifies the base, which must have the form B for a real bignum or 0JB for a complex bignum where B<2*16
• the 1st element indicates the number of places that the radix point is shifted to the left (a negative number indicates that the radix point is shifted to the right)
• the 2nd element is 1 for a negative real bignum and zero otherwise (even in the complex case).

The remaining elements provide the base B expansion of the abslute value of the number in the real case (i.e. B complement notation is not used), and the base 0JB expans of the number in the complex case.

A bigpoly array is a special type of bignum array in which the 1st axis is reserved for the coefficients of a polynomial in one variable, say x, such that the ith element is the coefficient of the ith power of x.

APL Primitive Functions

BA←ima BA           ⍝ 11○ over bignums
BA←rea BA           ⍝ 9○ over bignums
BA←cnj BA           ⍝ monadic + over bignums
BA←BA add BA        ⍝ dyadic + over bignums
BA←{BA} sub BA      ⍝ - over bignums
BA←BA mul BA        ⍝ dyadic × over bignums
BA←{BA} cat BA      ⍝ ⍪ over bignums
BA←rav BA           ⍝ , over bignums (monadically: , also works).
BA←{A} trn BA       ⍝ ⍉ over bignums
BA←{A} rot BA       ⍝ ⌽ over bignums
BA←{A} rof BA       ⍝ ⊖ over bignums
BA←{A} pic BA       ⍝ ⊃ over bignums
BA←{A} sqd BA       ⍝ ⌷ over bignums
A←BA eql BA         ⍝ = over Bignums
A←BA neq BA         ⍝ ≠ over Bignums
A←BA leq BA         ⍝ ≤ over Bignums
A←BA geq BA         ⍝ ≥ over Bignums
A←BA gth BA         ⍝ > over Bignums
A←BA lth BA         ⍝ < over Bignums
BA←flo BA           ⍝ monadic ⌊ over bignums
BA←cel BA           ⍝ monadic ⌈ over bignums
BA←BA min BA        ⍝ dyadic ⌊ over bignums
BA←BA max BA        ⍝ dyadic ⌈ over bignums
BA←abs BA           ⍝ monadic | over bignums
BA←{A} rho BA       ⍝ ⍴ over bignums
BA←{BA} eps BA      ⍝ ∊ over bignums
BA←BA ind BA        ⍝ dyadic ⍳ over bignums
BA←rol BA           ⍝ monadic ? over bignums
BA←tke BA           ⍝ dyadic ↑ over bignums
BA←drp BA           ⍝ dyadic ↓ over bignums 
BA←spl BA           ⍝ monadic ↓ over bignums
BA←mix NBA          ⍝ monadic ↑ over bignums
BA←{BA} div BA      ⍝ ÷ over bignums
BA←BA mod BA        ⍝ | over bignums
BA←snh BA           ⍝ 5○ over bignums
BA←cis BA           ⍝ 12○ over bignums
BA←tan BA           ⍝ 3○ over bignums
BA←sin BA           ⍝ 1○ over bignums

APL Primitive Operators

BA←BA bf dot bf BA  ⍝ f.g over bignums
BA←BA bf out BA     ⍝ ∘.f over bignums
BA←bf red BA        ⍝ f/ over bignums
BA←bf scn BA        ⍝ f\ over bignums
BA←bf rdf BA        ⍝ f⌿ over bignums
BA←bf scf BA        ⍝ f⍀ over bignums
BA←BA bf pop bg BA  ⍝ f⍣g over bignums
BA←{BA}bf rop k BA  ⍝ f⍤k over bignums

Numerical Algorithms

PA←PA pmul PA       ⍝ × over bigpolys
BA←mrp BA           ⍝ Miller-Rabin primality test
BA←sgp BA           ⍝ Sophie-Germain primality test
BA←{BA}rsg BA       ⍝ Creates random Sophie-Germain prime
BA←{BA}rpr BA       ⍝ creates random prime

Hashing

Cyphers

⍺ ⍵←key message ⋄ A←A AES.ecr A ⍝AES encrypt
⍺ ⍵←key message ⋄ A←A AES.dcr A ⍝AES decrypt

Protocols

Application Utilities

H←{B} hex A
A or BA←b64 BA or A ⍝ base 64 

Converts an integer array S into a hexadecimal string representing the data in row major order. Each element is assumed to represent B bits of data. If B is not provided, then the largest value in the array is used to calculate the number of bits to use per element.

Developer's Guide

Working with the Mystika code base involves writing tests in the tests/ directory and writing code in the [a-z].cd files in the root directory. Code is loaded into the mystika workspace using the LOAD function. The UT and util namespaces provide testing harness and utility function support for developers.

Useful Developer Functions

util.test <name> ⍝ Run the <name>_tests.dyalog test in tests/
util.TEST        ⍝ Run all tests in tests/
util.pp          ⍝ Equivalent to ⊢ but with a display as a side-effect
LOAD             ⍝ Load the latest mystika source into the workspace