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Given is a DHKE algorithm. The modulus p has 1024 bit and a is a generator of a subgroup where ord(a) = 2160.
1. What is the maximum value that the private keys should have?
2. How long does the computation of the session key take on average if one modular multiplication takes 700 μs, and one modular squaring 400 μs? Assume that the public keys ahev already been computed.
3. One well-known acceleration technique for discrete logarithm systems uses short primitive elements. We assume now that a is such a short element (e.g., a 16-bit integer). Assume that modular multiplication with a takes now only 30 μs. How long does the computation of the public key take now? Why is the time for one modular squaring still the same as above if we apply the square-and-multiply algorithm?
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