Design of Reliable and Secure Devices Realizing Shamir's Secret Sharing

Shamir's secret sharing scheme is an effective way to distribute secret to a group of shareholders. The security of the unprotected sharing scheme, however, can be easily broken by cheaters or attackers who maliciously feed incorrect shares during the secret recovery stage or inject faults into hardware computing the secret. In this paper, we propose cheater detection and identification schemes based on robust and algebraic manipulation detection (AMD) codes and m-disjunct matrices (superimposed codes). We present the constructions of codes for cheater detection and identification and describe how the cheater identification problem can be related to the classic group testing algorithms based on m-disjunct matrices. Simulation and synthesis results show that the proposed architecture can improve the security level significantly even under strong cheating attack models with reasonable area and timing overheads.