Efficient algorithm to solve DLP from partial knowledge of the Key

The discrete logarithm problem (DLP) is assumed to be hard from computational point of view. Side channel attacks are used to reveal information about the key if proper countermeasures are not used. We study the discrete logarithm problem assuming that partial information about the key is known. K. Gopalakrishnan et al. provided algorithms to solve the discrete logarithm problem for generic groups which are considerably better than square-root attack on the whole key when one contiguous bits of the key is revealed. This paper provides algorithms which will work when more than one contiguous bits of the key are revealed with time complexity of (unknownbits) order square root 2.