Introduction to Cryptography with Open-Source Software

292 Cryptography with Open-Source Software

Sage Exercises

25. Mars orbits the sun and rotates in such a way that there are 668 Mar-

tian days in a Martian year. How many Martians are required so the

probability that two of them share a birthday is (a) 0.5 ? (b) 0.9?

26. Use the simplified MASH (SMASH) of q uestion 23 as follows: for a

message m, considered as a large integer, define y

i

to be the “digits” of

m in base n. This can be obta ined in Sage with

sage: y = m.digits(n)

Define

sage: p = next_prime(2^40)

sage: q = next_prime(3^26)

Use these values to hash the phrase:

Now is the winter of our discontent made glorious summer

by this sun of York.

and use the ...