Hideki Yoshikawa

Masahiro Kaminaga, Hideki Yoshikawa, Arimitsu Shikoda et al.

The Rabin cryptosystem has been proposed protect the unique ID (UID) in radio-frequency identification tags. The Rabin cryptosystem is a type of lightweight public key system that is theoretetically quite secure; however it is vulnerable to several side-channel attacks. In this paper, a crashing modulus attack is presented as a new fault attack on modular squaring during Rabin encryption. This attack requires only one fault in the public key if its perturbed public key can be factored. Our simulation results indicate that the attack is more than 50\% successful with several faults in practical time. A complicated situation arises when reconstrucing the message, including the UID, from ciphertext, i.e., the message and the perturbed public key are not relatively prime. We present a complete and mathematically rigorous message reconstruction algorithm for such a case. Moreover, we propose an exact formula to obtain a number of candidate messages. We show that the number is not generally equal to a power of two.

Masahiro Kaminaga, Hideki Yoshikawa, Toshinori Suzuki

A new fault attack, double counting attack (DCA), on the precomputation of $2^t$-ary modular exponentiation for a classical RSA digital signature (i.e., RSA without the Chinese remainder theorem) is proposed. The $2^t$-ary method is the most popular and widely used algorithm to speed up the RSA signature process. Developers can realize the fastest signature process by choosing optimum $t$. For example, $t=6$ is optimum for a 1536-bit classical RSA implementation. The $2^t$-ary method requires precomputation to generate small exponentials of message. Conventional fault attack research has paid little attention to precomputation, even though precomputation could be a target of a fault attack. The proposed DCA induces faults in precomputation by using instruction skip technique, which is equivalent to replacing an instruction with a no operation in assembly language. This paper also presents a useful "position checker" tool to determine the position of the $2^t$-ary coefficients of the secret exponent from signatures based on faulted precomputations. The DCA is demonstrated to be an effective attack method for some widely used parameters. DCA can reconstruct an entire secret exponent using the position checker with $63(=2^6-1)$ faulted signatures in a short time for a 1536-bit RSA implementation using the $2^6$-ary method. The DCA process can be accelerated for a small public exponent (e.g., 65537). The the best of our knowledge, the proposed DCA is the first fault attack against classical RSA precomputation.