Error-Detecting and Fault-Tolerant Structures for ECC

For constrained devices, elliptic curve cryptography (ECC) is an attractive choice because it achieves the same level of security with a much smaller key size in comparison with other schemes such as those that are based on integer factorization or discrete logarithm. For security reasons, especially to provide resistance against fault-based attacks, it is very important to verify the correctness of computations in ECC applications. In this report, fault-tolerant and error-detecting elliptic curve cryptosystems are considered. Error detection may be a sufficient countermeasure for many security applications. However, fault-tolerant characteristic enables a system to perform its normal operation in spite of faults. This will result in more reliable systems where faults may occur due to natural causes. For the purpose of detecting errors due to faults, a number of schemes based on the point-on-the-curve checking, time redundancy, and hardware redundancy are presented. A combination of the point-on-thecurve checking and time or hardware redundancy can be used for detecting errors with a very high probability during the computation of the elliptic curve scalar multiplication (ECSM). Additionally, we show that using dual modular redundancy (DMR) and the point-on-the-curve checking, it is possible to have a fault-tolerant structure for the ECSM. If certain conditions are met, this scheme is more efficient than others such as the well-known triple modular redundancy.