# Science:Math Exam Resources/Courses/MATH312/December 2008/Question 05 (b)

MATH312 December 2008

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### Question 05 (b)

Alice wants Bob to send her a secret integer P between 0 and 1250 using RSA encryption with key ${\displaystyle \displaystyle (e,n)=(1189,1271)}$ (so the exponent is 1189 and the modulus is 1271, it is way too small to be really secure, but basic RSA encryption and decryption methods still work of course).

(b) To obtain P from C, Alice first computes an inverse ${\displaystyle \displaystyle d\in \mathbb {Z} }$ of e modulo ${\displaystyle \displaystyle \phi (n)}$, since she created the key, she knows that ${\displaystyle \displaystyle 1271=31\cdot 41}$ (in fact, the prime factorization of n can easily be found since it is so small). Compute such a d.

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