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Category > Statistics Posted 23 Apr 2017 My Price 2.00

How would you use the law

How would you use the law ab mod n = ((a mod n)(b mod n)) mod n to reduce to 13 the number of multiplications required to compute 3577 mod 83 from 76 multiplications?

Can you reduce it any further?

 

Answers

Alpha Geek
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Status NEW Posted 23 Apr 2017 04:04 PM My Price 2.00

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file 1492966141-Answer.docx preview (78 words )
H-----------ow -----------wou-----------ld -----------you----------- us-----------e t-----------he -----------law----------- ab----------- mo-----------d n----------- = -----------((a----------- mo-----------d n-----------)(b----------- mo-----------d n-----------)) -----------mod----------- n -----------to -----------red-----------uce----------- to----------- 13----------- th-----------e n-----------umb-----------er -----------of -----------mul-----------tip-----------lic-----------ati-----------ons----------- re-----------qui-----------red----------- to----------- co-----------mpu-----------te -----------357-----------7 -----------mod----------- 83----------- fr-----------om -----------76 -----------mul-----------tip-----------lic-----------ati-----------ons-----------? C-----------an -----------you----------- re-----------duc-----------e i-----------t a-----------ny -----------fur-----------the-----------r? ----------- An-----------swe-----------r: ----------- T-----------he -----------use-----------r -----------can----------- re-----------duc-----------e i-----------t t-----------o 7----------- mu-----------lti-----------pli-----------cat-----------ion-----------s. ----------- T-----------he -----------cal-----------cul-----------ati-----------ons----------- ar-----------e a-----------s g-----------ive-----------n b-----------elo-----------w: ----------- 7-----------7= -----------100-----------110-----------1 =----------- 2^-----------6+2-----------^3+-----------2^2-----------+2^-----------0 =-----------64+-----------8+4-----------+1 ----------- N-----------ow,----------- 35-----------^(6-----------4+8-----------+4+-----------1) -----------mod----------- 83----------- = -----------35^-----------77 -----------mod----------- 83----------- =(-----------35^-----------64 -----------*35-----------^8 -----------*35-----------^4 -----------*35-----------^1)----------- mo-----------d 8-----------3 =----------- ((-----------35^-----------64 -----------mod----------- 83-----------)(3-----------5^8-----------
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