Cryptographic Hardware

Compute x as far as possible without a calculator. Where appropriate, make use of a smart decomposition of the exponent:

a. x 3¹⁰ mod 13

b. x 7¹⁰mod 13

c. 3^x 2 mod 5 (use trial and error for this. As you see, there are infinite answers in the form of k+4n, k being the first number you find and n being an integer)

The last problem is called a Discrete Logarithm Problem and points to a hard problem which we discuss later as part of Elliptic Curve Cryptography. The security of many public-key schemes is based on the hardness of solving the discrete logarithm for large numbers, e.g., with more than 1000 bits. 4. Find all integers n between 0