Sidebar – Computing Large Numbers mod n
This presentation is the property of its rightful owner.
Sponsored Links
1 / 3

Sidebar – Computing Large Numbers mod n PowerPoint PPT Presentation


  • 108 Views
  • Uploaded on
  • Presentation posted in: General

Sidebar – Computing Large Numbers mod n In public key cryptography, we have to compute large numbers, like: 6 43 mod 13 Calculating such large numbers on a hand calculator (or on the PC calculator often results in getting a floating point approximation. This

Download Presentation

Sidebar – Computing Large Numbers mod n

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Sidebar computing large numbers mod n

Sidebar – Computing Large Numbers mod n

In public key cryptography, we have to compute large numbers, like:

643 mod 13

Calculating such large numbers on a hand calculator (or on the PC

calculator often results in getting a floating point approximation. This

isn’t much use since we need exact arithmetic.

These kinds of problems can be decomposed in to simpler forms by

direct manipulation. One method is repeated squaring.

Big Numbers


Sidebar computing large numbers mod n

Large Numbers mod n

For 643 mod 13, observe = (243 mod 13) x (343 mod 13). Also consider:

21 mod 13 = 2 mod 13 = 2

22 mod 13 = 4 mod 13 = 4

24 mod 13 = 42 mod 13 = 16 mod 13 = 3

28 mod 13 = (24)2 mod 13 = 32 mod 13 = 9

216 mod 13 = (28)2 mod 13 = 92 mod 13 = 81 mod 13 = 3

232 mod 13 = (216)2 mod 13 = 32 mod 13 = 9

So… 243 mod 13 = (232 x 28 x 22 x 21) mod 13

= (9 x 9 x 4 x 2) mod 13 = mod 13 = 11

Big Numbers


Sidebar computing large numbers mod n

Large Numbers mod n

For 343 mod 13:

31 mod 13 = 3 mod 13 = 3

32 mod 13 = 9 mod 13 = 9

34 mod 13 = 92 mod 13 = 81 mod 13 = 3

38 mod 13 = (34)2 mod 13 = 32 mod 13 = 9

316 mod 13 = (38)2 mod 13 = 92 mod 13 = 81 mod 13 = 3

332 mod 13 = (316)2 mod 13 = 32 mod 13 = 9

So… 343 mod 13 = (332 x 38 x 32 x 31) mod 13

= (9 x 9 x 9 x 3) mod 13 = 2187 mod 13 = 3

And 243 x 343 mod 13 = (11 x 3) mod 13 = 33 mod 13 = 7

Big Numbers


  • Login