Abstract: Martin Tompa and Heather Woll demonstrated that Shamir's Scheme is not secure against cheating and this attack is called Tompa-Woll attack. In this paper, we show that the Asmuth-Bloom's System is also not secure against strong cheating. A little modification of this scheme retains the security and efficiency of the original scheme and is secure against strong cheating.

Key words: threshold scheme, MDS code, Tompa-Woll attack