Build an RSA encoder

Question

Your task is to build a function in any language that takes a message m, an encryption e, and a modulus k (all positive integers), and takes m to the power of e modulo k. Your solution must not be a theoretical one, but one that would work on a reasonable computer such as your own, for RSA keys of currently used sizes such as 2048 bits.

Shortest code wins.

Answer 1

Python – 5

Python 3 built-in function pow have third parameter. So Python 3 already have built-in RSA encoder

r=pow

Answer 2

Here's my first attempt at actually golfing something here:

Python – 69 61 55

r=lambda m,e,k:1 if e==0 else m**(e%2)*r(m*m%k,e/2,k)%k

This is a simple exponentiation by squaring algorithm.

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02/15 13:17 – 61: Used lambda notation.
02/22 15:44 – 55: Removed some brackets as per grc's suggestions.

Answer 3

java (83 chars)

if input is of BigInteger type:

public BigInteger r(BigInteger m,BigInteger e,BigInteger k){return m.modPow(e,k);}

Answer 4

Husk, 7 bytes

!¡o%⁰*³

Try it online!

Function that takes arguments: arg1=m (message), arg2=k (key/modulus), arg3=e (exponent/encryption).

Encoding takes about 10 seconds on [Try it online!] with a message of 12345678910, a 2048-bit key/modulus of 17335246217810680499565282364130282347913694411139706552337646969996795185310539972695213589521948877888710148108314183322475193115466538523720272848165926667358225384343389288464059692412384746831929390686202279817642231618920311152771862965772849228722380926373552800043250590230507345247504584516585217552163181827225685419709962073929610117852078754818132187957128758451536498778247147713136878727238232838512570562685513074673965992921930197584545660069134797478016576085619884280636191861425890311213983668804147423192923778212236303196414996652277121672303217925415867248268691221399027188630076689585126618899, and exponent/encryption of 65537.

Decoding is significantly longer when (as is usual) the decryption exponent d is much larger than the encryption exponent e. But we can check that it works using small values: m=123, k=257 and e=7 (for which the decryption exponent d=55):
Try encoding
Try decoding

Answer 5

Nibbles, 4 bytes (8 nibbles)

=_`.@%*_

=_`.@%*_        # full program
=_`.@%*_$@      # with implicit args added
  `.            # repeatedly apply (while results are unique)
    @           # starting with arg2:
      *_$       #   multiply arg2 by result-so-far
     %   @      #   and modulo by arg1
=_              # finally, return result at index given by arg3

Full program that takes arguments: arg1=k (key/modulus), arg2=m (message), arg3=e (exponent/encryption).

Encoding is fast (screenshot below shows a message of 12345678910, a 2048-bit key/modulus, and exponent/encryption of 65537).
Decoding is significantly longer when (as is usual) the decryption exponent d is much larger than the encryption exponent e. But we can check that it works using small values: m=123, k=257 and e=7 (for which the decryption exponent d=55).