This paper investigates the security of constant weight countermeasures, which aim to produce indistinguishable leakage from sensitive variables and intermediate variables, assuming a constant Hamming distance and/or Hamming weight leakages. To investigate the security of recent countermeasures, contrary to many related studies, we assume that the coefficients of the simulated leakage models follow a normal distribution so that we may construct a model with approximately realistic leakages. First, using our simulated leakage model, we demonstrate security holes in these previous countermeasures. Subsequently, in contrast to the hypotheses presented in previous studies, we confirm the resistance of these countermeasures to a standard correlation power analysis (CPA). However, these countermeasures can allow a bitwise CPA to leak a sensitive variable with only a few thousand traces.

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Since passive leakage information analysis and active fault injection attacks on naive implementation of the Rivest, Shamir, and Adelman (RSA) cryptosystem can be used to retrieve a secret key, several countermeasures against these attacks have been developed. In this paper, we point out that the horizontal correlation power analysis (HCPA) attack can be applied to the square-multiply ladder exponentiation algorithm and its variants, which are used for secure RSA implementation. Furthermore, we propose a novel exponentiation algorithm to defeat previous implementation attacks, as well as the HCPA attack, in particular. This algorithm is designed to overcome weakness against the HCPA attack by adopting an intermediate message update technique based on an extended modulus. We can employ the proposed exponentiation algorithm to implement a secure Chinese remainder theorem-based RSA (CRT-RSA) cryptosystem by thwarting the Bellcore attack.

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