Differential operators

Problem attached.

Eigenvalue problem

Problem attached.

Green's function for an eigenvalue problem

Problem attached.

Game Theory

In the two-player game of Two Stacks, a deck of cards (with the joker added, for a total of 53 cards) is randomly divided into two piles. The two players take turns removing cards from one pile or the other. On a player's turn, that player may remove any positive number of cards from a single pile. The object of the game is to r ...continues

Obtaining orthonormal eigenfunctions

Problem attached.

RSA Cipher

Alice chooses two large prime numbers p and q. She finds their product, m=pq which is public. She also finds n= (p-1)(q-1) which is private. She chooses e which is a number relatively prime to n and finds d= the inverse of e (mod n). The number e is public and the number d is private. When Bob wants to send a message x (a number ...continues

Congruency

solve for a and b 4a + b = 1 (mod 5) a + b = 2 (mod 5) check answers for a and b by substituting into the original equations

Diffie Helman Key Exchange

Alice and Bob want to do a Diffie- Helman Key Exhange. The public base is 5 and the public modulus is 11. Suppose Alice chooses a = 2 and Bob Chooses b=3. What common key did they calculate? What does the security of the Diffie Helman Key exhange depend upon?

Cipher

Is the ADFGVX cipher a substitution cipher, transposition cipher or both? Explain. Explain Kerkhoff's principle. What does the security of a RSA cipher depend upon?

Cryptogram

Solve the following cryptogram doing the following steps: 1. frequency count 2. do you think it is monoalphabetic substitution, polyalphabetic subsitution, or transposition? 3. Is this a clear decision? 4. Solve based on the above info. DVOLL PULID ZIWGL ZDLIO WULFM WVWFM WVWFK LMULF IVHHV MGRZO SFNZM UIVVW LNHGS VUR ...continues