Algebraic manipulation detection codes and their applications for design of secure cryptographic devices

Cryptographic devices are vulnerable to fault injection attacks. All previous countermeasures against fault injection attacks based on error detecting codes assume that the attacker cannot simultaneously control the fault-free outputs of a device-under-attack and error patterns. For advanced attackers who are able to control both of the above two aspects, traditional protections can be easily compromised. In this paper, we propose optimal algebraic manipulation detection (AMD) codes based on the nonlinear encoding functions and the random number generators. The proposed codes can provide a guaranteed high error detecting probability even if the attacker can fully control the fault-free outputs of a device-under-attack as well as the error patterns. As a case study, we present the protection architectures based on AMD codes for multipliers in Galois fields used for the elliptic curve cryptography. The results show that the proposed architecture can provide a very low error masking probability at the cost of a reasonable area overhead. The protected multiplier has no latency penalty when the predictor is pipelined.