In this paper we introduce a novel algorithm for Gaussian integer exponentiation that significantly improves its performance. We compare the performance of Gaussian integer exponentiation (using new and existing algorithms) to real integer exponentiation both analytically and experimentally. We demonstrate that the algorithms based on the Gaussian Integer exponentiation have significant advantages over the corresponding algorithms based on the real integer exponentiation. Moreover, we show that the new algorithm is significantly faster. Therefore, the new algorithm could speedup Public Key Discrete Logarithm Based cryptographic algorithms by about 40% with a possibility for further improvements.
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