A method and system for determining sequence parameters to limit cycle attack in time-line sequences associated with digital signature technologies is disclosed. The method comprises the steps of determining a pair of values associated with a modulus value for generating said sequence, wherein said values are non-equal prime numbers of a known size, selecting a root value of said sequence and selecting a third value for determining the order of said sequence. In one aspect of the invention, each of the pair of values used to determine the modulus is a safe prime number.