CryptoCalculator

This is a piece of work created to help with identifying and understanding the beginner levels of IT Security and encryption techniques

The largest value that this Calculator can calculate is 9007199254740991 due to standard Javascript restrictions

For the Large Number Calculator (with no limits apart from the speed that your computer takes to process)
you can visit the other page Big Integer Calculator

*The Big Number Calculator also has more calculators and examples to work with...

*This is a work in progress and still incomplete...

Modular Calculators:

Mod Calculation

PowerMod Calculation

Modular Inverse:

General Tools:

Generate Random Prime number

Generate Random Number

Elgamal Examples:

Sender has: y, g, p values

Receiver has all values and has secret x value

Tools:

Encode:

Step 1 - Calculate y (y):

Step 2 - Calculate k (k):

Step 3 - Calculate Code 1 (C1):

Step 4 - Calculate Code 2 (C2):

Step 4 (Exponential) - Calculate Code 2 (C2):

Decode:

Step 1 - Calculate (encoded) k (k):

Step 2 - Modular Inverse:

Step 3 - Decrypt Message:

Step 3 - Exponential Decrypt Message:

Get Value A:

Get Message:

Paillier Examples:

Sender has: n,g Values

Receiver has all values including secret λ and μ values

Tools:

*If you want to manually enter the values, enter them in the inputs instead of clicking on compute button

Encode:

Get λ (Lambda) value:

Calculate K Value :

Calculate μ (Mu) Value :

Encrypt Message (c) :

Decode:

Decrypt Message (M) :

Project Details:

CryptoCalculator

Description

This project was put together during the mid semester break to help identify and understand the underlying concepts, formulas and principles within the Cryptography classes.

index.html - https://cryptocalc.com.au/original-content/originalcalc.html

This is the original site, it holds the standard base calculations in javascript, however due to the javascript large number limitations it can not hadle substantially large numbers, so it ony contains the basic concepts and tools, such as:

The javascript files have been broken up into specific types of calculations to help users identify how the formulas are calculated in the javascript language. These are using basic javascript mathematic calculations in order to help other users understand the underlying concepts.

If you want to view the specific javascript calculations, here are the links to the speicic javascript files. All the methods have comments explaing what they do, how they function and the values required for them to function:

BigIntCalculator.html - https://cryptocalc.com.au/original-content/bigintcalculator/bigintcalculator.html

This is a child of the original site, it has the same initial calculations, however this version uses the BigInteger.js javascript library which allows uses to do calculations on substantially large numbers. Due to this, further examples have been added as they can use substantially larger numbers for their calculations.

*The Paillier version for secret addition of numbers will be added shortly for reference.

The javascript files for these are also split up based on type of calculations to help users understand the concepts, however as they use the BigInteger.js library, the code is not using standard mathematic formulas. The BigInteger.js library can be found at: https://github.com/peterolson/BigInteger.js and it also lists a full explanation and examples of the library methods in the readme on the page.

The conversion for large numbers between binary and decimal calculations were attained from an answer on stack overflow:
https://stackoverflow.com/questions/39334494/converting-large-numbers-from-binary-to-decimal-and-back-in-javascript

Main Site - https://cryptocalc.com.au/

This is the new main site and holds all the original calculators, plus extra General tools, hashing examples, IPFS examples and more.

The main site is now the updated version to follow and use as it has substantially higher calculations, resources and tools.

Enjoy, and hope it helps fellow users in their cryptographic learnings and education.

Base:	Exponent:	Modulus:
	b^e MOD m =

public key g (g) :	private key x (x) :	Public key p (p) :
	*[ y ]* = g^x MOD p =

public key y (y) :	Random Number r (r) :	Public key p (p) :
	*[ k ]* = y^r MOD p =

public key g (g) :	Random Number r (r) :	Public key p (p) :
	*[ C1 ]* = g^r MOD p =

Cipher Text m (m) :	K Value k (k) :	Public key p (p) :
	*[ C2 ]* = m k* MOD p =

Random prime number maximum (max) :
	Random Prime Number =

Code 1 (C1) :	Private Key x (x) :	Public key p (p) :
	(decoded) *[ k ]* = C1^x MOD p =

Modular inverse number (k^-1) :	Code 2 C2(C2) :	Public key p (p) :
	(message) *[ m ]* = k^-1C2 MOD p =

Modular inverse number (k^-1) :	(Step 4 (Exponential) - Calculate) Code 2 C2(C2) :	Public key p (p) :
	*[ a ]* = k^-1C2 MOD p =

Enter Value A (a) :	Value G (g) :	Public key p (p) :
	(message) *[ m ]* = g^m MOD p =

[ p ] Generate a random prime number for (p) :	Enter maximum value of number then click compute:
[ q ] Generate a random prime number based on (p) :	Enter maximum value of number then click compute:
[ n ] Calculate based on (p) and (q) :
[ g ] Generate (g) based on (n) :
[ r ] Generate random number (r) :	Enter maximum value of number then click compute:
[ m ] Create message to encode (m):

Enter Value P (p) :	Value Q (q) :
	*[ λ ]* = lcm(p - 1, q - 1) =

Enter Value G (g) :	Value λ (Lambda) (λ) :	Value N (n) :
	[ k ] = L(g^λ MOD n²) =

Base g (g) :	Base r (r) :	Exponent and Modulus n (n) :	Message to encrypt m (m) :
		[ c ] = g^mrⁿ MOD n² =

Encrypted message c (c) :	Exponent λ (λ) :	Modulus n (n) :	Value μ(μ) :
		[ m ] = L(c^λMOD n²).μ MOD n =

CryptoCalculator - 2020

*This is a work in progress and still incomplete...

Contents:

Modular Calculators:

Mod Calculation

PowerMod Calculation

Modular Inverse:

General Tools:

Generate Random Prime number

Generate Random Number

Elgamal Examples:

Tools:

Encode:

Step 1 - Calculate y (y):

Step 2 - Calculate k (k):

Step 3 - Calculate Code 1 (C1):

Step 4 - Calculate Code 2 (C2):

Step 4 (Exponential) - Calculate Code 2 (C2):

Decode:

Step 1 - Calculate (encoded) k (k):

Step 2 - Modular Inverse:

Step 3 - Decrypt Message:

Step 3 - Exponential Decrypt Message:

Get Value A:

Get Message:

Paillier Examples:

Tools:

Encode:

Get λ (Lambda) value:

Calculate K Value :

Calculate μ (Mu) Value :

Encrypt Message (c) :

Decode:

Decrypt Message (M) :

Project Details: