create a fast modular exponent function

[krishnajalan]

this function run in log(N) time complexity and log(N) space complexity to find the modular exponent and can be used cryptographic encryption to find the modular exponent of a really large prime numer

[coveralls]

Coverage decreased (-2.3%) to 95.75% when pulling ac92910 on krishnajalan:patch-1 into f27b20f on warner:master.

[coveralls]

Coverage decreased (-0.2%) to 97.772% when pulling 9226ce3 on krishnajalan:patch-1 into f27b20f on warner:master.

[tomato42]

how much faster it is than the built-in pow()? how much faster it is than pow() when gmpy2 is used?

I've done some quick benchmarks and it's at least 4 times slower with the native ints on python3, do you see something different?

[krishnajalan]

how much faster it is than the built-in pow()? how much faster it is than pow() when gmpy2 is used?

I've done some quick benchmarks and it's at least 4 times slower with the native ints on python3, do you see something different?

now made some tweeks might be faster now
and this method is the one used for encrytion and decryption algorythm
this is better than built in pow as this can handle much larger prime number (more than 100 digit number)

[tomato42]

now it doesn't work, ans=1 is missing

also, it is slower than pow:

a = 2
x = 0x2341b79adf72ef90a532158BFD3E2B9C8CF51558903BA0D0F8435A021FFF5E91479E
p = 0xEEAF0AB9ADB38DD69C33F80AFA8FC5E86072618775FF3C0B9EA2314C9C256576D674DF7496EA81D3383B4813D692C6E0E0D5D8E250B98BE48E495C1D6089DAD15DC7D7B46154D6B6CE8EF4AD69B15D4982559B297BCF1885C529F566660E57EC68EDBC3C05726CC02FD4CBF4976EAA9AFD5138FE8376435B9FC61D2FC0EB06E3

In [9]: %timeit fast_modular_exponentiation(a, x, p)
7.01 ms ± 2.65 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

In [10]: %timeit pow(a, x, p)
638 µs ± 2.8 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)

[krishnajalan]

now this is fast please review this code

a = 2
x = 0x2341b79adf72ef90a532158BFD3E2B9C8CF51558903BA0D0F8435A021FFF5E91479E
p = 0xEEAF0AB9ADB38DD69C33F80AFA8FC5E86072618775FF3C0B9EA2314C9C256576D674DF7496EA81D3383B4813D692C6E0E0D5D8E250B98BE48E495C1D6089DAD15DC7D7B46154D6B6CE8EF4AD69B15D4982559B297BCF1885C529F566660E57EC68EDBC3C05726CC02FD4CBF4976EAA9AFD5138FE8376435B9FC61D2FC0EB06E3

%timeit fast_modular_exponentiation(a, x, p)
2.12 µs ± 6.39 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)

%timeit pow(a, x, p)
798 µs ± 4.51 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)

[tomato42]

it's also providing incorrect result:

In [8]: pow(a, x, p)
Out[8]: 156585191525109838650514497544841306938118786727686521188924477616074565750827971867070903274582757259308907082099809400189995273960711551098573085830248220735659354382108924600679178686704643615034564481430785405384599047848897245930269730454359626054001725047726611533932270804253803224884355215811899509232

In [9]: fast_modular_exponentiation(a, x, p)
Out[9]: 1

[krishnajalan]

now this is fast please review this code

a = 2
x = 0x2341b79adf72ef90a532158BFD3E2B9C8CF51558903BA0D0F8435A021FFF5E91479E
p = 0xEEAF0AB9ADB38DD69C33F80AFA8FC5E86072618775FF3C0B9EA2314C9C256576D674DF7496EA81D3383B4813D692C6E0E0D5D8E250B98BE48E495C1D6089DAD15DC7D7B46154D6B6CE8EF4AD69B15D4982559B297BCF1885C529F566660E57EC68EDBC3C05726CC02FD4CBF4976EAA9AFD5138FE8376435B9FC61D2FC0EB06E3

%timeit fast_modular_exponentiation(a, x, p)
2.12 µs ± 6.39 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)

%timeit pow(a, x, p)
798 µs ± 4.51 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)

[tomato42]

now this is fast please review this code

a = 2
x = 0x2341b79adf72ef90a532158BFD3E2B9C8CF51558903BA0D0F8435A021FFF5E91479E
p = 0xEEAF0AB9ADB38DD69C33F80AFA8FC5E86072618775FF3C0B9EA2314C9C256576D674DF7496EA81D3383B4813D692C6E0E0D5D8E250B98BE48E495C1D6089DAD15DC7D7B46154D6B6CE8EF4AD69B15D4982559B297BCF1885C529F566660E57EC68EDBC3C05726CC02FD4CBF4976EAA9AFD5138FE8376435B9FC61D2FC0EB06E3

%timeit fast_modular_exponentiation(a, x, p)
2.12 µs ± 6.39 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)

%timeit pow(a, x, p)
798 µs ± 4.51 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)

this is more than 100 time faster

return 1 would be even faster, doesn't make it particularly useful, does it?

1. why are you talking about prime numbers? this is trying to use the basic square and multiply algorithm
2. why you think that the built-in pow doesn't use this or even more efficient algorithm? and why do you think that pow can't handle large numbers (not that 100 decimal digits is large...)
3. this code is not py2 and py3 compatible
4. you're modifying code that is explicitly marked as deprecated and unused while not removing the deprecation and updating rest of the library code to start using it
5. this code is missing any test coverage
6. it's not following the formatting guidelines