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Comparative Modular Exponentiation with Randomized Exponent to Resist Power Analysis Attacks

  • Research Article - Computer Engineering and Computer Science
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Abstract

We present a secure variant of modular exponentiation implemented in RSA and CRT-RSA to resist power analysis attacks. For speeding up the computation, modular exponentiation is generally done through “squaring and multiplication” according to the binary bit of the secret exponent. This is popularly known as straight forward method. However, such computation leaves behind distinct traces of power consumption leading to power analysis attacks. These attacks were so powerful that they could reveal the secret exponent or the key challenging the vulnerability of any cryptosystem. In this work, we have enhanced the security of modular exponentiation by first randomizing the exponent or the secret key and then executing comparative bitwise squaring and multiplication. Our proposed work could be implemented in left-to-right or right-to-left without any modification of the algorithm which removed the dependency of “squaring and multiplication” on the bits of the key. As RSA decryption has more security privilege, we have implemented our proposed work only while decrypting the message. However, it can be used during encryption too. The randomized key, bit-independent squaring–multiplication and comparative modular exponentiation would generate non-uniform and random power traces resisting it from power analysis attacks.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Assam University, Silchar, India

    Hridoy Jyoti Mahanta & Ajoy Kumar Khan

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  1. Hridoy Jyoti Mahanta
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  2. Ajoy Kumar Khan
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Correspondence to Hridoy Jyoti Mahanta.

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Mahanta, H.J., Khan, A.K. Comparative Modular Exponentiation with Randomized Exponent to Resist Power Analysis Attacks. Arab J Sci Eng 42, 3423–3434 (2017). https://doi.org/10.1007/s13369-017-2517-z

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  • DOI: https://doi.org/10.1007/s13369-017-2517-z

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