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# IDEA reasons for multiplication mod 2^16 + 1

Posted on 2004-09-27
Medium Priority
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Hi.. i m not even sure if this is the correct place for this question or not...

but..

i was looking at the International Data Encryption Algorithm, and it has three vital parts to it are:

bit-by-bit exclusive-OR of two 16-bit sub-blocks

addition of integers modulo 2^16 where the 16-bit sub-block is treated as an unsigned integer

multiplication of integers modulo (2^16) + 1 where the 16-bit sub-block is treated as an unsigned integer except that the all-zero sub-block is treated as representing 2^16

why is it that in IDEA the addition is modulo 2^16 as opposed to say, (2^16) + 1 and why is multiplication (2^16)+1 as opposed to say 2^16?

Thanks,
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Question by:sr11130107
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Expert Comment

ID: 12166623
Because 2^16+1 is prime number
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Author Comment

ID: 12170939
well, yea. .but besides that trivial fact.. and then why is addition only 2^16..??

mabe it was just a design that suited it more. but was just curious..

if no more feedbakc, i'll motion for a delete..

thanks,
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LVL 62

Accepted Solution

gheist earned 200 total points
ID: 12172330
Mostly it is not used because it is heavily patented until 2011.
You are not cryptoanalyst as far as I see, basicaly multiplying by 2^n is same as bit shifting ( very simple to inverse )
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