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Memory Address Side-Channel Analysis on Exponentiation

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Book cover Information Security and Cryptology - ICISC 2014 (ICISC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 8949))

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Abstract

Side-channel analysis aims at cryptography implementation by exploiting and analyzing side-channel information. Side-channel leakage of software implementation does not only depend on operators (instruction) and operands (value) but also on where operators and operands are called or stored in the memory. However, in contrast to the leakage of the operator and operand values, the exploitable leakage caused by the memory address is quite small. Side-channel analysis aiming at memory address usually needs a huge number of samples to eliminate the algorithmic noise. This paper presents a new attack method exploiting the leakage from consecutive addresses when accessing multiple-byte operands during evaluation of an exponentiation. By folding the observed side-channel leakage, one measurement is enough to perform statistical side-channel analysis and successfully reveal the secret key. Since only one measurement is sufficient, this attack even works in the presence of common side-channel countermeasures such as exponent randomization and message blinding.

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Notes

  1. 1.

    Actually, the analysis in [3] targets \(\mathtt {a}_i \times \mathtt {b}_j\) in a long-integer multiplication, but the same idea can be applied to Montgomery multiplication.

  2. 2.

    This paper targets the right-to-left exponentiation algorithm, and the operands \(\mathtt {A}\) and \(\mathtt {A}'\) are identical to \(\mathtt {S}\) and \(\mathtt {Y}\) in Fig. 1(B), storing in the addresses \(\mathsf {Addr}(\mathtt {a}_i) = \mathtt {0x0344} + i\) and \(\mathsf {Addr}(\mathtt {a}'_i) = \mathtt {0x0385}+ i\), respectively.

  3. 3.

    In the second experiment, the two operands of the multiplication in line 04 of Fig. 1(B) are swapped, i.e., replacing \(\mathtt {Y} = \mathtt {Y} \times \mathtt {S} ~\hbox {mod}~\mathtt {M}\) by \(\mathtt {Y} = \mathtt {S} \times \mathtt {Y} ~\hbox {mod}~\mathtt {M}\).

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Acknowledgments

The author wishes to thank Marc Stöttinger for his kindness to provide many useful discussions. He also likes to thank the anonymous referees for their helpful comments which improve both presentation and technical content.

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Authors and Affiliations

  1. Physical Analysis and Cryptographic Engineering (PACE), Nanyang Technological University, Singapore, Singapore

    Chien-Ning Chen

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  1. Chien-Ning Chen
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Correspondence to Chien-Ning Chen .

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Editors and Affiliations

  1. Sejong University, Seoul, Korea, Republic of (South Korea)

    Jooyoung Lee

  2. Kookmin University, Seoul, Korea, Republic of (South Korea)

    Jongsung Kim

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Chen, CN. (2015). Memory Address Side-Channel Analysis on Exponentiation. In: Lee, J., Kim, J. (eds) Information Security and Cryptology - ICISC 2014. ICISC 2014. Lecture Notes in Computer Science(), vol 8949. Springer, Cham. https://doi.org/10.1007/978-3-319-15943-0_25

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  • DOI: https://doi.org/10.1007/978-3-319-15943-0_25

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