montgomery's modular multiplication a...

montgomery's modular multiplication algorithm

Posted in the Cryptography Forum


Mumbai, India

#1 Dec 8, 2008
hey m involved in one project tht uses this rsa encryption technique. i understood the basic methodology, but cant understand the montgomery's reduction technique they use to perform modular multiplication. It uses all that bit shifting or sth else which i cudn decipher. I wud be very greatful if someone could give a simple explanation with an example on how it works.

Mumbai, India

#2 Dec 8, 2008
somebody pls..

Butler, NJ

#3 Dec 9, 2008
arkus, if you are are in a hurry, the most important thing to understand is that Montgomery multiplication is not necessary, in RSA. It makes RSA run faster, but everything will work fine without it.

If you want to understand Montgomery multiplication, I found two nice web pages:

If you can find Montgomery's original paper, "Multiplication without trial division," it is a great piece of writing: very clear to understand.

But your post refers to "bit shifting" -- this is a basic technique of modular exponentiation, whether or not a Montgomery speed-up is used.

For an explanation of this basic modular exponentiation algorithm, see

I highly recommend that you do your best, to understand the math used in these procedures.


#4 Jan 19, 2009
can anyone suggest the site where i can get the complete verilog tutorials....

Gwangju, Korea

#5 Nov 6, 2011
I am confused in the Montgomery modular multiplication and Montgomery reduction. Can anyone tell me what is the difference/relation between these two ?

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