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In this paper, we propose a novel key recovery attack against secure ECDSA signature generation employing regular table-based scalar multiplication. Our attack exploits novel leakage, denoted by collision information, which can be constructed by iteratively determining whether two entries loaded from the table are the same or not through side-channel collision analysis. Without knowing the actual value of the table entries, an adversary can recover the private key of ECDSA by finding the condition for which several nonces are linearly dependent by exploiting only the collision information. We show that this condition can be satisfied practically with a reasonable number of digital signatures and corresponding traces. Furthermore, we also show that all entries in the pre-computation table can be recovered using the recovered private key and a sufficient number of digital signatures based on the collision information. As case studies, we find that fixed-base comb and T_SM scalar multiplication are vulnerable to our attack. Finally, we verify that our attack is a real threat by conducting an experiment with power consumption traces acquired during T_SM scalar multiplication operations on an ARM Cortex-M based microcontroller. We also provide the details for validation process.

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Advanced collision-based single trace attacks which can be applied on simple power analysis resistant scalar multiplications become virtual threat on elliptic curve cryptosystems recently as their practical experimental results are increasingly reported in the literature. Since such attacks are based on detecting collisions of data dependent leakage caused by underlying long integer multiplications, so-called global shuffling countermeasure which breaks such collision correlation by independently randomizing the execution order of unit operations such as single precision multiplication and carry propagation, is considered as promising countermeasure if theoretical randomness of shuffling order is guaranteed. In this paper, we firstly analyze the practical security of the global shuffling long integer multiplications by exhibiting a combined single trace attack on software implementations on an ARM Cortex-M4 microcontroller. Our combined attack consists of a simple power analysis for revealing random permutation vectors which enables later collision-based single trace attack. First we demonstrate how to reveal random permutation vectors for carry propagation process of whole global shuffling long integer multiplications within a single power trace by simple power analysis accompanied with straightforward substitution of power consumption samples. Then we perform collision-based single trace attacks after rearranging the order of subtraces for unit carry propagations based on revealed permutation vectors. Since the vulnerability to simple power analysis is originated from the if-statement for selection of proper entries of the permutation vectors, we propose a novel countermeasure which eliminates such selection with simple addition and modulus operation and also demonstrate practical result achieving regularity in power trace patterns. INDEX TERMS Cryptography, digital signatures, elliptic curves, public key, side-channel attacks.

Until recently, power analysis is one of the most popular research issues among various side channel analyses. Since Differential Power Analysis had been first proposed by Kocher et al., various practical power analyses correspond with software/hardware cryptographic devices have been proposed. In this paper, we analyze vulnerability of countermeasure against power analysis exploiting single power trace of public cryptographic algorithm. In ICICS 2010, Clavier et al. proposed Horizontal Correlation Analysis which can recover secret information from a single exponentiation trace and corresponding countermeasures. "Blind operands in LIM", one of their countermeasures, exploits additive blinding in order to prevent leakage of intermediate value related to secret information. However, this countermeasure has vulnerability of having power leakage that is dependant with the message known by an adversary. In this paper, we analyzed vulnerabilities by three attack scenarios and proved them by practical correlation power analysis experiments.