To improve your understanding of RSA, hash functions, MAC and key distribution.
To develop problem-solving and design skills. To improve written communication skills.
Questions
An integer encoded message M and a pair of RSA keys are provided as following: M = 314159265?????93 (please replace ????? with the last five digits of your student ID)
Private key: < n,d > Public key: < n,e >
n = 11396311342906819133245180752504625094447926145771153608337005942535340 831151082124611648733795917345423093120647809492578196651328326613421541984 374544599265256494866003364648970813971670451048426724934881335069848815008
57942197501
e = 65537 d = 20729576806810227945651433503304642530313216592724403339332811669890870 507980537712665435487675836653308618504240738644446969730044899317107941502 247799584959444798172916891463972996495752944622965018659022099059225470003
8562058305
(d) Sign the message by calling your above implemented Sign function. Print the signature here.
(a) Describe an efficient attack against this method.
(b) Suggest a countermeasure to this attack.
Jaiden: < n,e1 >, < n,d1 > Jiajia: < n,e2 >, < n,d2 >
Answer the following questions with detailed process and/or justification.
(a) Describe the scheme in steps.
(b) How do A and B know that the key is freshly generated?
(c) How could A and B know that the key is not available to other users in the system?
(d) Does this scheme ensure the authenticity of both A and B? Justify your answer.
M1,M2,M3,...,Mm such that Mi < n. The hash is constructed by XOR the results of encrypting all blocks. For example, the hash value of a message consisting of three blocks is calculated by
Does this hash function satisfy each of the following requirements? Justify your answers (with examples if necessary).
(a) Variable input size
(b) Fixed output size
(c) Efficiency (easy to calculate)
(d) Preimage resistant
(e) Second preimage resistant
(f) Collision resistant
Submission and Evaluation
• We expect your work to be neat — parts of your submission that are difficult to read or decipher will be deemed incorrect. Make sure that you have enough time towards the end of the assignment to present your solutions carefully. Time you put in early will usually turn out to be more productive than a last-minute effort.
Please see https://academicintegrity.unimelb.edu.au
