How does the Mongomery Algorithm work?

meran_kud

2/1/24, 12:09 AM

can someone please explain to me what's the role of montgomery reduction algorithm and how to implement it in python. I wrote the code below to calculate a*b mod m but it doesn't seem to work well.

def montgomery(a,b,m):

bin_m=format(m,'b')
R=pow(2,len(bin_m))

a_prim= a *(R % m)
b_prim= b *(R % m)

reverse_R=euc(R,m)

if inverse_R<0:
    inverse_R+=m

c_prim=(a_prim*b_prim)*reverse_R
result=c_prim*reverse_R

return print(result)

0 + 3

modular-arithmetic

montgomery-multiplication

cryptocurrency

Myria

2/1/24, 12:14 AM

If you're using Python, there's no reason to do this yourself, because Python has arbitrary-precision integers built into the language. Just do `pow(b, e, m)` to compute $b^e \pmod m$.

Rohit Gupta

2/1/24, 12:30 AM

You could ask this on Super User

fgrieu

2/1/24, 6:49 AM

Have a look at [this](https://crypto.stackexchange.com/a/84332/555). Note that unless you break the representation of integers into chunks, you can't use Montgomery arithmetic, only simulate it. Also notice that the Montgomery method for Elliptic Curve scalar multiplication is not directly related to Montgomery arithmetic. If you have more questions on the math, [edit](https://crypto.stackexchange.com/posts/104005/edit) the question, toning down the python aspects of it, and removing the _cryptocurrency_ tag.

Elon Musk

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EN: How does the Mongomery Algorithm work?

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