Horizontal Correlation Analysis on Exponentiation

Abstract. We introduce in this paper a technique in which we apply correlation analysis using only one execution power curve during an ex-ponentiation to recover the whole secret exponent manipulated by the chip. As in the Big Mac attack from Walter, longer keys may facili-tate this analysis and success will depend on the arithmetic coprocessor characteristics. We present the theory of the attack with some practical successful results on an embedded device and analyze the efficiency of classical countermeasures with respect to our attack. Our technique, which uses a single exponentiation curve, cannot be pre-vented by exponent blinding. Also, contrarily to the Big Mac attack, it applies even in the case of regular implementations such as the square and multiply always or the Montgomery ladder. We also point out that DSA and Diffie-Hellman exponentiations are no longer immune against CPA. Then we discuss the efficiency of known countermeasures, and we finally present some new ones.