The University of Melbourne School of Computing and Information Systems COMP90043: CRYPTOGRAPHY AND SECURITY Mid Semester Test, Second Semester, 2020 Test Duration: 40 minutes Test + 5 minutes Reading + 15 minutes Uploading. Instructions to Students: • Total marks for the test is 50 (Worth 10% of the final mark in the subject). • Note that the total time to read, complete the work, scan and upload your responses to this test is 1 hour. The last 15 minutes is for uploading your work. • Test will be open on 5.15PM and you must submit by 6.15PM Australian Eastern Standard Time (AEST). A late submission will attract a penalty of 2.5 marks per minute late. • The test will have two parts: Part A is a quiz on canvas, Part B is this assignment and will have three questions. • The test is open book, which means you may only use course materials pro- vided via the LMS or the text book but must not use any other resource including the Internet. • You also must not contact or communicate with any other person (other than teaching team) or make use of the Internet. • Solutions must be written on blank A4 page paper with pen and pencil. You must write your solutions to each question on a new sheet of paper by clearly identifying the question number. • You must not use tablet or any electronic device to generate your solution. • Scanning instructions are already made available on Canvas in an announce- ment. COMP90043 Cryptography and Security School of Computing and Information Systems Part A Please complete the Quiz on Canvas available at Assignments - Mid-Semester Test - Part A Part B: This Assignment: 1. Basic Numbers (a) [5 Marks] Find 35−1 mod 96 using Extended Euclidean algorithm dis- cussed in the subject. Show step-by-step working. (b) [5 Marks] Find the smallest non-negative remainder of (127136000075+36)28 divided by 111. Show your working. HINT: You may need to use various simplifying ideas discussed in lectures and workshop including Euler’s and Fermat’s theorems. 2. RSA (a) [4 Marks] Explain how we may factorise an RSA modulus n if we know a number a such that a2 mod n = 1. (b) [6 Marks] A pair of RSA keys can be generated using two prime numbers p and q, as discussed in the subject. However, in this question you will consider a version of RSA involving three prime numbers p, q and r (such that n = p × q × r), which follows a similar process to generate a pair of encryption and decryption keys, e and d. Show the equations for generating such a pair of keys for the modified RSA crypto system. Using the parameters p = 23, q = 29 and r = 31, find the minimum possible encryption key e and then compute the corresponding decryption key d. As discussed in the subject, remember to present the keys in the form of < n, e > and < n, d >. Copyright c© University of Melbourne 2020 Page 2 of 3 COMP90043 Cryptography and Security School of Computing and Information Systems 3. The following equations and figure describe one of the standard modes of usage of symmetric key encryption. Figure 1: A Standard Mode of Encryption Encryption: Let IV is the Initial Vector obtained from the Nonce generator. C1 = P1 ⊕ EK [IV ]. Cj = Pj ⊕ EK [Cj−1 ⊕ Pj−1], j > 1. (a) [2 marks] What is the name of this mode? (b) [2 Marks] Briefly explain (in no more than two sentences) the purpose of using the Nonce in this mode. (c) [4 Marks] Using the notations available in the above figure, complete the following decryption functions. Decryption: P1 = .............................. Pj = .............................. (d) [2 Marks] What is the effect on the decrypted plaintext if a one-bit error occurred in the transmission of a ciphertext block Cj? How far does the error propagate? END OF EXAMINATION Copyright c© University of Melbourne 2020 Page 3 of 3