Modular desk calculator (mdc)

A re-implementation of the GNU program dc, in modular arithmetic.

As of right now, strings, arrays and macros aren't implemented.

The supported operations are:

• <number>, _<number>: pushes the number number onto the stack. If it is preceded by _, pushes the negative value for it.
• m: pops a value from the stack and sets it as the modulus for all subsequent operations; if set to 0 (default), then no modulus is applied. This number is referred to as m
• M: pushes onto the stack the value of m
• %: pops a number x from the stack and pushes back x mod m
• +: pops two numbers a and b and pushes back (a + b) mod m (or a + b if m = 0)
• -: pops two numbers a and b and pushes back (a - b) mod m (or a - b if m = 0)
• *: pops two numbers a and b and pushes back (a * b) mod m (or a * b if m = 0)
• /: pops two numbers a and b and pushes back (a / b) mod m (or a // b if m = 0); requires that gcd(b, m) divides a
• ^: pops two numbers a and b and pushes back (a ^ b) mod m (or a ^ b if m = 0; in that case, b must be less than ULONG_MAX)
• C: pops two numbers a and b and pushes back lcm(a, b)
• G: pops two numbers a and b and pushes back gcd(a, b)
• d: duplicates the value on top of the stack
• z: pushes on the stack the current length of the stack
• v: pops a number x from the stack and computes the modular square root of x, see Modular square root for more information (Note: composite moduli and moduli congruent to 1 mod 8 haven't been implemented yet.)
• ~: pops a number x from the stack and pushes back -x mod m (or m if m = 0)
• f: prints the entirety of the stack
• p: prints the top value of the stack
• n: pops a number from the stack and prints it, without a newline
• c: clears the stack
• r: swaps the position of the top two values of the stack
• s<r>: pops x from the stack and stores in on the top of the register <r> (overriding the previous value)
• S<r>: pops x from the stack and pushes it on top of the register <r>'s stack (shadowing the previous value)
• l<r>: pushes on the stack the top value of the register <r>
• L<r>: pops x from the stack of the register <r> and pushes it onto the stack (un-shadowing values below it)

Spaces are optional, except between numbers. I really recommend reading through dc's documentation if you aren't somewhat familiar with it already.

Installation

To compile and use this software, you will need git, GNU Make, a C compiler and the GNU MP library (gmp on Arch Linux).

First, clone this repository, then compile it with make:

git clone https://github.com/adri326/mdc
cd mdc
make

The final binary will be put in build/mdc. You can copy it into a directory that is in your PATH to have the command mdc available everywhere.

Running

Simply execute the mdc binary; it will then read input from stdin and print output to stdout.

If you aren't piping anything into mdc, then it will act as a kind of terminal; you may write and edit commands, and submit them by pressing enter. To exit, press Ctrl+D to send the EoF character.

Example usage

31m # Set the modulus to 31
10 # Push 10
2* p # Prints 20
2* p # Prints 40%31 = 9
4* p # Prints (9*4) % 31 = 5

The following expression computes (23*(3*1+40))² - 2 mod 103:

103m
1 3* 40 + # (3*1 + 40)
23* 2^ # (23*(3*1+40))²
2- # (23*(3*1+40))² - 2
p # Prints 31

The following encrypts and decrypts a message using RSA:

2010942103422233250095259520183 sp # p
3503815992030544427564583819137 sq # q
lplq*p sn # n
lp1-lq1-Cm # Compute λ(n) and use it as modulo
2 16^ 1+ d se # e = 2^16+1
1r/p sd # d = e^-1 mod λ(n)

lnm # Use n as modulo
36762444129608 le ^p # Encode the message with (n, e); here the message is the decimal version of "Hello!"
ld ^p # Decode the message

For comparison, here is how you would have to do it using vanilla dc:

2010942103422233250095259520183 sp # p
3503815992030544427564583819137 sq # q
lplq*p sn # n
lp1- lq1- # Load p-1 and q-1
[dSarLa%d0<a]dsax+ # Compute gcd(p-1, q-1), thank you Wikipedia for the expression
lp1- lq1- *r/ sl # Compute λ(n) and store it
2 16^ 1+ d se # e = 2^16+1
lldsm le dsa1sv[dsb~rsqlbrldlqlv*-lvsdsvd0<x]dsxxldd[dlmr+]sx0>x p sd # Computes d = e^-1 mod λ(n), thanks Rosetta stone for this expression

36762444129608 le ln |p # Encode the message with (n, e); here the message is the decimal version of "Hello!"
ld ln |p # Decode the message

Warranty

This software is provided as-is, there is no warranty, to the extent permitted by law. See LICENSE.md for more detail.

This software is not fit for cryptographic uses, use it at your own risk.