# HW #5 (30 Mar. 2015) (Pdf format)

```COMP547B Homework set #5 Due Monday April 13th, 2015
Exercises (from Katz and Lindell’s book)
[10%]
[10%]
Hint for 11.6 : Prove that if it is not CPA-secure then the DiffieHellman problem is efficiently solved.
[10%]
More on back…
[10%]
[10%]
[10%]
[10%]
More on back…
MAPLE QUESTIONS
Let
e≔N≔12801889219865986943874426789172837719929575398179139903346
0102259322494388756606728373121043154809790249663472677206622549
2472049090344014040948783013844255405121563940725271958261549105
6895127372123401970340184655821416714383833567438594837829393436
445708175846840391647287652219983832401360628720836954408208209
be an RSA public modulus ( e=N as in Cocks‘ variation ).
[10%]
1) Without factoring N, provide a message m together with its RSA
signature σ such that m ends with “2015” in base 10. Show that σ is a valid
signature.
[10%]
2) Without factoring N, check that the exponent
e’≔9998582802019135990088028686968303570983958400372883846244557
7041064925905995005216889007572898641811594513334409291762876864
91104489407462355371113514648093
is also valid to verify signed messages. Show at least 5 examples.
[10%]
3) Given e and e’, factor N. What is special about the factors of N ??
More on back…
```