In 1990, the present authors proposed the first ID-based non-interacrive key sharing scheme (ID-NIKS) based on the discrete logarithm problem (DLP) over a composite number $n$. With a rapid progress of computer system for the last two decades, ID-NIKS based on DLP over $n$ would have more chance to be applied practically. However, there existed no secure ID-NIKS based on DLP over $n$ against the square-root attack when $n$ is a product of three prime numbers. In this paper, we propose an ID-NIKS based on DLP over a product of three prime numbers which can circumvent the square-root attack.