https://github.com/fcasal/cryptoutils.jl

Cryptography and number-theory primitives in Julia
https://github.com/fcasal/cryptoutils.jl

continued-fractions cryptography julia number-theory prime-numbers

Last synced: about 1 month ago
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Cryptography and number-theory primitives in Julia

• Host: GitHub
• URL: https://github.com/fcasal/cryptoutils.jl
• Owner: fcasal
• License: mit
• Created: 2019-07-22T00:22:51.000Z (over 5 years ago)
• Default Branch: master
• Last Pushed: 2020-07-07T23:59:56.000Z (over 4 years ago)
• Last Synced: 2024-10-12T23:22:35.892Z (about 1 month ago)
• Topics: continued-fractions, cryptography, julia, number-theory, prime-numbers
• Language: Julia
• Homepage:
• Size: 66.4 KB
• Stars: 5
• Watchers: 2
• Forks: 1
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# CryptoUtils

[![Dev](https://img.shields.io/badge/docs-dev-blue.svg)](https://fcasal.github.io/CryptoUtils.jl/dev/)

## Features

This package supports a number of cryptographic and number theory related primitives:

 * generation of random prime numbers and safe primes;

 * Jacobi and Legendre symbols;

 * modular square roots;

 * continued fractions of rationals and convergents;

 * "bytes to number" and "number to bytes" conversion functions;

 * RSA attacks:

    * Wiener's attack with Dujella's extension;

    * Factor `n = p*q`, given `e` and `d`.

## Installation

To install the package, simply run from the julia REPL:

```

julia> ]add CryptoUtils

```

## Documentation

Access the full [documentation](https://fcasal.github.io/CryptoUtils.jl/dev/).

## Example

```julia

julia> using CryptoUtils

julia> p = random_prime(512); q = random_prime(512); n = p*q # generate semiprime n

131745220523048272797760331579564741491214753542423769574982847786514776153155250573474208964071358407384440164414712528658264269591534035958596966591477455650082238340858337257106511821924740760868219278777077341070367621453029038918351903399126114774879588852878367966142856170535138849910785240708139225987

julia> e = 65537

65537

julia> d = invmod(e, (p-1)*(q-1))  # compute RSA decryption exponent

32362883641310315451899592262377172791965856192371946631485250568611645044625881242387678564972226360689108476233462883544705990145324113781489121643593621753163078450834460663942035227770596133499206721223993086064885467845603112395435294663436699341967664046213003429586468421266641276398515468366056248785

julia> factor_with_ed(n, e, d)  # factor n with e and d

(11209007052907094316298587866392085453240213973638699831846376613053337678939099626874977325024647359864974367465362518878257931790980202563932031187056729, 11753513928682888932534842071560505691719602160983337271901213762089936749492510218729499032535262339600976674663969869808030961514878135483359095845990203)

julia> p

11209007052907094316298587866392085453240213973638699831846376613053337678939099626874977325024647359864974367465362518878257931790980202563932031187056729

julia> q

11753513928682888932534842071560505691719602160983337271901213762089936749492510218729499032535262339600976674663969869808030961514878135483359095845990203

```