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3. Compute x as far as possible without a calculator. Where appropriate, make use of a smart decomposition of the exponent: x E310 mod 13

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3. Compute x as far as possible without a calculator. Where appropriate, make use of a smart decomposition of the exponent: x E310 mod 13 710 mod 13 32 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 Crvptography. 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

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