6.6 Let p = 227. The element a = 2 is primitive in Zap*. (a) Compute...

 

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6.6 Let p = 227. The element a = 2 is primitive in Zap*. (a) Compute a 32, a 40, a 59 and a 156 modulo p, and factor them over the factor base {2, 3, 5, 7, 11}. (b) Using the fact that log 2 = 1, compute log 3, log 5, log 7 and log 11 from the factorizations obtained above (all logarithms are discrete logarithms in Zp* to the base a). (c) Now suppose we wish to compute log 173. Multiply 173 by the "random" value 2177 mod p. Factor the result over the factor base, and proceed to compute log 173 using the previously computed logarithms of the numbers in the factor base. 6.6 Let p = 227. The element a = 2 is primitive in Zap*. (a) Compute a 32, a 40, a 59 and a 156 modulo p, and factor them over the factor base {2, 3, 5, 7, 11}. (b) Using the fact that log 2 = 1, compute log 3, log 5, log 7 and log 11 from the factorizations obtained above (all logarithms are discrete logarithms in Zp* to the base a). (c) Now suppose we wish to compute log 173. Multiply 173 by the "random" value 2177 mod p. Factor the result over the factor base, and proceed to compute log 173 using the previously computed logarithms of the numbers in the factor base.