Montgomery reduction: Difference between revisions

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=={{header|Sidef}}==

{{trans|zkl}}

<lang ruby>func montgomeryReduce(m, a) {

{

a += m if a.is_odd

a >>= 1

} * m.as_bin.len

a % m

}

var m = 750791094644726559640638407699

var t1 = 323165824550862327179367294465482435542970161392400401329100

var r1 = 440160025148131680164261562101

var r2 = 435362628198191204145287283255

var x1 = 540019781128412936473322405310

var x2 = 515692107665463680305819378593

say("Original x1: ", x1)

say("Recovererd from r1: ", montgomeryReduce(m, r1))

say("Original x2: ", x2)

say("Recovererd from r2: ", montgomeryReduce(m, r2))

print("\nMontgomery computation of x1^x2 mod m: ")

var prod = montgomeryReduce(m, t1/x1)

var base = montgomeryReduce(m, t1)

for (var exponent = x2; exponent ; exponent >>= 1) {

prod = montgomeryReduce(m, prod * base) if exponent.is_odd

base = montgomeryReduce(m, base * base)

}

say(montgomeryReduce(m, prod))

say("Library-based computation of x1^x2 mod m: ", x1.powmod(x2, m))</lang>

{{out}}

<pre>

Original x1: 540019781128412936473322405310

Recovererd from r1: 540019781128412936473322405310

Original x2: 515692107665463680305819378593

Recovererd from r2: 515692107665463680305819378593

Montgomery computation of x1^x2 mod m: 151232511393500655853002423778

Library-based computation of x1^x2 mod m: 151232511393500655853002423778