Improved Atomicity to Prevent HCCA on NIST Curves
Poulami Das, Debapriya Basu Roy, Debdeep Mukhopadhyay · 2016
The Big Mac attack showed that an RSA implementation, protected with conventional side-channel countermeasures can be exploited on the basis of an operand sharing property of field multiplications with a single trace of side-channel leakage. In fact this property of operand sharing among field multiplications underlying the computation of an exponentiation algorithm can be utilized to break a wide range of RSA and elliptic curve implementations, thus imposing a serious threat. The ECC algorithms designed with side-channel atomic blocks to protect against simple side-channel analysis are seen to vulnerable to an advanced form of horizontal attack by detecting this operand sharing property among field operations. We demonstrate how to resist an atomicity-equipped ECC algorithm by transforming the algorithm into a safe form which is based on rearranging the order of operands in field multiplications underlying an addition or doubling, keeping the atomicity property intact.