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.

  • \$\begingroup\$ How are you measuring memory usage? Does this implicitly forbid using big integer libraries unless they come with documented guarantees about their memory usage? \$\endgroup\$ Feb 15, 2013 at 18:47
  • 2
    \$\begingroup\$ (And if you're going to post a challenge about RSA, why not make it interesting by asking for an implementation of real RSA as opposed to academic useless-for-protecting-secrets RSA?) \$\endgroup\$ Feb 15, 2013 at 18:48
  • \$\begingroup\$ @PeterTaylor: Big-integer libraries are fine. The main point of the limit is to prevent people from trying to store the entire exponentiated number and then evaluating it modulo m. \$\endgroup\$
    – Joe Z.
    Feb 15, 2013 at 18:50
  • \$\begingroup\$ @PeterTaylor: Also, you can pose the question that includes PKCS #1 if you want. \$\endgroup\$
    – Joe Z.
    Feb 15, 2013 at 18:53

5 Answers 5


Python – 5

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

  • \$\begingroup\$ Looks like we have a winner. I didn't know that. :\ \$\endgroup\$
    – Joe Z.
    Feb 23, 2013 at 20:20
  • \$\begingroup\$ In fact, the solution has a length of 0. Just use function pow for RSA encoding/decoding \$\endgroup\$
    – AMK
    Feb 23, 2013 at 20:33
  • \$\begingroup\$ Nope, it's still length 3 because you need to describe it. :P \$\endgroup\$
    – Joe Z.
    Feb 23, 2013 at 20:34
  • 1
    \$\begingroup\$ Imho, this solution has a char count of 5. By just providing pow, the criteria 'build a function' is not satisfied. \$\endgroup\$
    – codeporn
    Feb 25, 2013 at 11:16
  • \$\begingroup\$ Yeah, I suppose that's true. \$\endgroup\$
    – Joe Z.
    Feb 27, 2013 at 13:38

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.

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

  • \$\begingroup\$ I believe the question specifies that the function should be named RSA \$\endgroup\$
    – Shmiddty
    Feb 15, 2013 at 17:50
  • \$\begingroup\$ Sorry, that was unclear on my part. \$\endgroup\$
    – Joe Z.
    Feb 15, 2013 at 18:11
  • 1
    \$\begingroup\$ You can save a few chars by removing unnecessary spaces and brackets: r=lambda m,e,k:1if e==0 else m**(e%2)*r(m*m%k,e/2,k)%k. And you might also be able to do this, but I haven't tested it: r=lambda m,e,k:e<1or m**(e%2)*r(m*m%k,e/2,k)%k. It uses e<1 instead of e==0 and or instead of if ... else. \$\endgroup\$
    – grc
    Feb 16, 2013 at 0:30
  • 1
    \$\begingroup\$ In most C-derived languages, */% have equal precedence and are evaluated left-to-right. \$\endgroup\$ Feb 22, 2013 at 20:59
  • 1
    \$\begingroup\$ @Joe Zeng: Yes, but True behaves as 1 when it is used with arithmetic operators. \$\endgroup\$
    – grc
    Feb 23, 2013 at 0:45

java (83 chars)

if input is of BigInteger type:

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

Husk, 7 bytes


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


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).
enter image description here 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). enter image description here


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