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In this paper we address the problem of protecting elliptic curve scalar multiplication implementations against side-channel analysis by using the atomicity principle. First of all we reexamine classical assumptions made by scalar multiplication designers and we point out that some of them are not relevant in the context of embedded devices. We then(More)
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 facilitate this analysis and success will depend on the arithmetic coprocessor characteristics. We(More)
The recent results presented by Moradi et al. on AES at CHES 2010 and Witteman et al. on square-and-multiply always RSA exponentiation at CT-RSA 2011 have shown that collision-correlation power analysis is able to recover the secret keys on embedded implementations. However, we noticed that the attack published last year by Moradi et al. is not efficient on(More)
Embedded exponentiation techniques have become a key concern for security and efficiency in hardware devices using public key cryptography. An exponentiation is basically a sequence of multiplications and squarings, but this sequence may reveal exponent bits to an attacker on an unprotected implementation. Although this subject has been covered for years,(More)
In this paper, we study the fixed-point scalar multiplication operation on elliptic curves in the context of embedded devices prone to physical attacks. We propose efficient algorithms based on Yao and BGMW algorithms that are suited for embedded computing, with various storage-efficiency trade-offs. In particular, we study their security towards(More)
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