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Physical security of elliptic curve cryptography

Abstract : Elliptic Curve Cryptography (ECC) has gained much importance in smart cards because of its higher speed and lower memory needs compared with other asymmetric cryptosystems such as RSA. ECC is believed to be unbreakable in the black box model, where the cryptanalyst has access to inputs and outputs only. However, it is not enough if the cryptosystem is embedded on a device that is physically accessible to potential attackers. In addition to inputs and outputs, the attacker can study the physical behaviour of the device. This new kind of cryptanalysis is called Physical Cryptanalysis. This thesis focuses on physical cryptanalysis of ECC. The first part gives the background on ECC. From the lowest to the highest level, ECC involves a hierarchy of tools: Finite Field Arithmetic, Elliptic Curve Arithmetic, Elliptic Curve Scalar Multiplication and Cryptographie Protocol. The second part exhibits a state-of-the-art of the different physical attacks and countermeasures on ECC.For each attack, the context on which it can be applied is given while, for each countermeasure, we estimate the lime and memory cost. We propose new attacks and new countermeasures. We then give a clear synthesis of the attacks depending on the context. This is useful during the task of selecting the countermeasures. Finally, we give a clear synthesis of the efficiency of each countermeasure against the attacks.
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Submitted on : Thursday, July 23, 2015 - 1:29:06 AM
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  • HAL Id : tel-01179584, version 1



Cédric Murdica. Physical security of elliptic curve cryptography. Cryptography and Security [cs.CR]. Télécom ParisTech, 2014. English. ⟨NNT : 2014ENST0008⟩. ⟨tel-01179584⟩



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