This paper proposes a discrete logarithm algorithm that largely reduces execution times of Pollard's Rho and Brent's algorithm in obtaining  from   ≡  . The proposed algorithm can be distinguished from the conventional Brent's algorithm by three major features: it sets an initial value as     in lieu of    ; replaces           pointer with   ←         ≤  ≤  for a Queue the size 10; and detects collision of     ′      instead of   . This

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... ueue method has reduced the execution time of Pollard's Rho algorithm with        by , and that of Brent's algorithm with     by .