On the use of Karatsuba formula to detect errors in GF((2 ⁿ) ²) multipliers

Galois fields are widely used in cryptographic applications. The detection of an error caused by a fault in a cryptographic circuit is important to avoid undesirable behaviours of the system that could be used to reveal secret information. One of the methods used to avoid these behaviours is the concurrent error detection. Multiplication in finite field is one of the most important operations and is widely used in different cryptographic systems. The authors propose in this study an error-detection method for composite finite-field multipliers based on the use of Karatsuba formula. The Karatsuba formula can be used in GF((2n)2) field to decrease the hardware complexity of the finite-field multiplier. The authors propose a novel finite-field multiplier with concurrent error-detection capabilities based on the Karatsuba formula. How the error-detection capabilities of this multiplier are able to face a wide range of fault-based attacks is also shown.