1. Show that given an RSA modulus N and ø(N), it is possible to factor N easily. Hint: you have two equations (involving ø(N) and N) and two unknowns (p and q). Write a sage function that takes as input an RSA modulus N and ø(N) and factors N. Use it to factor the following 2048-bit RSA modulus. Note: take care that there are no precision issues in how you solve the problem; double-check your factorization! N = 133140272889335192922108409260662174476303831652383671688547009484 253235940586917140482669182256368285260992829447207980183170174867 620358952230969986447559330583492429636627298640338596531894556546 013113154346823212271748927859647994534586133553218022983848108421 465442089919090610542344768294481725103757222421917115971063026806 587141287587037265150653669094323116686574536558866591647361053311 046516013069669036866734126558017744393751161611219195769578488559 882902397248309033911661475005854696820021069072502248533328754832 698616238405221381252145137439919090800085955274389382721844956661 1138745095472005761807 phi = 133140272889335192922108409260662174476303831652383671688547009484 253235940586917140482669182256368285260992829447207980183170174867 620358952230969986447559330583492429636627298640338596531894556546 013113154346823212271748927859647994534586133553218022983848108421 465442089919090610542344768294481725103757214932292046538867218497 635256772227370109066785312096589779622355495419006049974567895189 687318110498058692315630856693672069320529062399681563590382015177 322909744749330702607931428154183726552004527201956226396835500346 779062494259638983191178915027835134527751607017859064511731520440 2981816860178885028680
1. Show that given an RSA modulus N and ø(N), it is possible to factor N easily. Hint: you have two equations (involving ø(N) and N) and two unknowns (p and q). Write a sage function that takes as input an RSA modulus N and ø(N) and factors N. Use it to factor the following 2048-bit RSA modulus. Note: take care that there are no precision issues in how you solve the problem; double-check your factorization! N = 133140272889335192922108409260662174476303831652383671688547009484 253235940586917140482669182256368285260992829447207980183170174867 620358952230969986447559330583492429636627298640338596531894556546 013113154346823212271748927859647994534586133553218022983848108421 465442089919090610542344768294481725103757222421917115971063026806 587141287587037265150653669094323116686574536558866591647361053311 046516013069669036866734126558017744393751161611219195769578488559 882902397248309033911661475005854696820021069072502248533328754832 698616238405221381252145137439919090800085955274389382721844956661 1138745095472005761807 phi = 133140272889335192922108409260662174476303831652383671688547009484 253235940586917140482669182256368285260992829447207980183170174867 620358952230969986447559330583492429636627298640338596531894556546 013113154346823212271748927859647994534586133553218022983848108421 465442089919090610542344768294481725103757214932292046538867218497 635256772227370109066785312096589779622355495419006049974567895189 687318110498058692315630856693672069320529062399681563590382015177 322909744749330702607931428154183726552004527201956226396835500346 779062494259638983191178915027835134527751607017859064511731520440 2981816860178885028680
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Question
3.
Transcribed Image Text:1. Show that given an RSA modulus N and ø(N), it is possible to factor N easily.
Hint:
you
have two equations (involving ø(N) and N) and two unknowns (p and g).
Write a sage function that takes as input an RSA modulus N and ø(N) and factors N. Use
it to factor the following 2048-bit RSA modulus. Note: take care that there are no precision
issues in how you solve the problem; double-check
your
factorization!
N = 133140272889335192922108409260662174476303831652383671688547009484
253235940586917140482669182256368285260992829447207980183170174867
620358952230969986447559330583492429636627298640338596531894556546
013113154346823212271748927859647994534586133553218022983848108421
465442089919090610542344768294481725103757222421917115971063026806
587141287587037265150653669094323116686574536558866591647361053311
046516013069669036866734126558017744393751161611219195769578488559
882902397248309033911661475005854696820021069072502248533328754832
698616238405221381252145137439919090800085955274389382721844956661
1138745095472005761807
phi = 133140272889335192922108409260662174476303831652383671688547009484
253235940586917140482669182256368285260992829447207980183170174867
620358952230969986447559330583492429636627298640338596531894556546
013113154346823212271748927859647994534586133553218022983848108421
465442089919090610542344768294481725103757214932292046538867218497
635256772227370109066785312096589779622355495419006049974567895189
687318110498058692315630856693672069320529062399681563590382015177
322909744749330702607931428154183726552004527201956226396835500346
779062494259638983191178915027835134527751607017859064511731520440
2981816860178885028680
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