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Authors:
James F. Kurose, Keith W. Ross
Chapter:
Security In Computer Networks
Exercise:
Problems
Question:8 | ISBN:9780132856201 | Edition: 6

Question

Consider RSA with p = 5 and q = 11.

a. What are n and z?

b. Let e be 3. Why is this an acceptable choice for e?

c. Find d such that de = 1 (mod z) and d < 160.

d. Encrypt the message m = 8 using the key (n, e). Let c denote the corre- sponding ciphertext. Show all work. Hint: To simplify the calculations, use the fact: [(a mod n) • (b mod n)] mod n = (a • b) mod n

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Answer

a. n=p*q=5*11=55 z=(p‐1)(q‐1)=(5‐1)(11‐1)=40

b. because it has no common factor with z and it is less than n.

c. d should obey ed – 1 is divisible by z: (ed‐1)/z = (3*d‐1)/40 ‐> d = 27

d. m^e = 8^3=512 c = m^e mod n = 512 mod 55 =17

Cite Ref. http://uniteng.com/wiki/lib/exe/fetch.php?media=classlog:computernetwork:hw7_report.pdf

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