Feature #6362: Modular exponentiation/inverse

• Status: Closed
• Assignee: matz (Yukihiro Matsumoto)
• Target version: -

[MartinBosslet (Martin Bosslet)]

I'd like to ask your opinion about adding two methods for modular
exponentiation/modular inverse to integer classes. Is this
functionality too specific or would this be a welcome addition?

[sdaubert (Sylvain Daubert)]

+1 : very helpful for cryptographic stuffs.

[mame (Yusuke Endoh)]

• Status changed from Open to Feedback
• Assignee set to MartinBosslet (Martin Bosslet)

Personally I like this proposal, but it seems to require:

• use cases (Well, personally I often use them for Project Euler :-)
• candidates of method name (pow_mod / inv_mod?)
• a detailed spec (especially corner cases, e.g., not coprime case, negative modulo, etc.)
• a patch
• other kinds of modular arithmetic are not needed? (add_mod, mul_mod, sqrt_mod, ...)

--
Yusuke Endoh [e-mail]

[MartinBosslet (Martin Bosslet)]

mame (Yusuke Endoh) wrote:

Personally I like this proposal, but it seems to require:

• use cases (Well, personally I often use them for Project Euler :-)

It would be incredibly helpful when implementing cryptographic primitives.
Apart from mathematics in general (and Project Euler in particular!) I have
little experience with other areas where it would be equally useful. One
could argue this should be in a gem, but since we already have excellent
Bignum support, I'd enjoy to see it even more excellent :)

• candidates of method name (pow_mod / inv_mod?)

Yes, I thought of them as well. If there would be no complaints...

• other kinds of modular arithmetic are not needed? (add_mod, mul_mod, sqrt_mod, ...)

Seems the right thing to do. GCD, modular shifts, etc. as well. I'll explore what
others like GMP or OpenSSL support and start from there.

• a detailed spec (especially corner cases, e.g., not coprime case, negative modulo, etc.)

Based on what I find out, I'll try to design an interface plus specs. Another question is
what particular algorithms to use for implementing each aspect. I'm currently catching
up on literature, although I'd be happy about suggestions, of course!

• a patch

Will do once there is a consensus on the specs!

-Martin

[nobu (Nobuyoshi Nakada)]

=begin
What about a new class, say Modulo?

m = Modulo.new(101, 11)
m.to_i #=> 2
m**4 #=> 5
=end

[mame (Yusuke Endoh)]

• Status changed from Feedback to Assigned
• Assignee changed from MartinBosslet (Martin Bosslet) to matz (Yukihiro Matsumoto)

Martin, thanks. Assigning it to matz.

nobu wrote:

What about a new class, say Modulo?

I guess, it would be slow, and therefore defeat the purpose.
But indeed it looks like the Ruby way.

Anyway, it mgiht be a good idea to start it with gem.

--
Yusuke Endoh [e-mail]

[MartinBosslet (Martin Bosslet)]

mame (Yusuke Endoh) wrote:

Martin, thanks. Assigning it to matz.

Sure, you're welcome :)

nobu wrote:

What about a new class, say Modulo?

Sounds really nice and it would extend better to arithmetic
in finite fields defined over irreducible polynomials or to
elliptic curves. This is where the initial proposal would
fall short eventually.

I guess, it would be slow, and therefore defeat the purpose.
But indeed it looks like the Ruby way.

Just for my understanding, why do you think it would be slow?
If it were written in C with access to Bignum internal representation,
would it still be slow?

Anyway, it mgiht be a good idea to start it with gem.

So there's no need for a spec right now, or would you still be
interested?

-Martin

[mame (Yusuke Endoh)]

• Target version set to 2.6

[spastorino (Santiago Pastorino)]

This would be a great thing to have +1000

[naruse (Yui NARUSE)]

• Target version deleted (2.6)

[msnm (Masahiro Nomoto)]

FYI:

• Modular exponentiation is implemented in Ruby 2.5 . https://ruby-doc.org/core/Integer.html#method-i-pow
• I created a patch gem to calculate a usual/modular multiplicative inverse. https://www.rubydoc.info/gems/numeric_inverse
• In heavy use, OpenSSL::BN is useful. https://ruby-doc.org/stdlib/libdoc/openssl/rdoc/OpenSSL/BN.html

[leahneukirchen (Leah Neukirchen)]

As of Python 3.8, modular inverses are supported by Python's pow function, which can take a mod argument, just like Ruby's.
https://docs.python.org/3/library/functions.html#pow

I therefore propose to add this feature as

n.pow(-1, m)

This currently throws an error (Integer#pow() 1st argument cannot be negative when 2nd argument specified), so should be possible to extend.

[nobu (Nobuyoshi Nakada)]

• Status changed from Assigned to Closed

Please file a new ticket.