Discrete logarithm problem
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Consider the multiplicative group of integers 1, 2,...,10, modulo 11^5. We want to compute the power we need to raise 2 to get 3.
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Solution Summary
We explain a simple lifting method to solve the discrete logarithm problem. Familiarity with Euler's totient function is assumed.
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We start with the multiplicative group of integers modulo 11 and work our way to modulo 11^5 using a lifting argument. Modulo 11 we have 2^3 = 8 = -3 Mod 11. And it turns out that 2 is a primitive element, we have 2^(5) = -1 Mod 11, so we find that 2^8 = 3 Mod 11. To set up the lifting method, note Euler's phi-function for ...
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