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Improving Non-profiled Attacks on Exponentiations Based on Clustering and Extracting Leakage from Multi-channel High-Resolution EM Measurements Read chapter Read first chapter

2015 | OriginalPaper | Chapter

Faster Mask Conversion with Lookup Tables

Authors : Praveen Kumar Vadnala, Johann Großschädl

Published in: Constructive Side-Channel Analysis and Secure Design

Publisher: Springer International Publishing

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Abstract

Masking is an effective and widely-used countermeasure to thwart Differential Power Analysis (DPA) attacks on symmetric cryptosystems. When a symmetric cipher involves a combination of Boolean and arithmetic operations, it is necessary to convert the masks from one form to the other. There exist algorithms for mask conversion that are secure against first-order attacks, but they can not be generalized to higher orders. At CHES 2014, Coron, Großschädl and Vadnala (CGV) introduced a secure conversion scheme between Boolean and arithmetic masking of any order, but their approach requires \(d=2t+1\) shares to protect against attacks of order t. In the present paper, we improve the algorithms for second-order conversion with the help of lookup tables so that only three shares instead of five are needed, which is the minimal number for second-order resistance. Furthermore, we also improve the first-order secure addition method proposed by Karroumi, Richard and Joye, again with lookup tables. We prove the security of all presented algorithms using well established assumptions and models. Finally, we provide experimental evidence of our improved mask conversion applied to HMAC-SHA-1. Simulation results show that our algorithms improve the execution time by 85 % at the expense of little memory overhead.

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previous chapter A Biased Fault Attack on the Time Redundancy Countermeasure for AES
next chapter Towards Evaluating DPA Countermeasures for Keccak K1012ECCAK on a Real ASIC
Footnotes
1
An S-box \(S: \{0,1\}^n \rightarrow \{0,1\}^m\) is said to be balanced if every element in \(\{0,1\}^m\) is image of exactly \(2^{n-m}\) elements in \(\{0,1\}^n\) under S.
 
2
We use different tables to store the actual value and the carries so that the security proof can be easily obtained as in [12].
 
3
Every call to the function Sec20B \(\rightarrow \) A_Word creates a new table and is useful for that particular word only. Hence, unlike the original method in [12], we do not reuse the table.
 
4
The only exception is for the row \(S(x_1 \oplus a)\), where we have four variables.
 
5
Note that, even though \(x^i\) and the carries are computed in clear, they are hidden amongst \(2^{l+2}-1\) dummy computations, which is the basis for the security of the original algorithm of Rivain, Dottax and Prouff [12].
 
6
We use different tables in the case of second-order masking, but we can re-use the table for first-order masking.
 
7
We observed that, for \(\ell < 4\), the algorithm from [7] performs better than ours.
 
Literature
1.
Beak, Y.-J., Noh, M.-J.: Differetial power attack and masking method. Trends Math. 8(1), 53–67 (2005)
2.
Chari, S., Jutla, C.S., Rao, J.R., Rohatgi, P.: Towards sound approaches to counteract power-analysis attacks. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 398–412. Springer, Heidelberg (1999)
3.
Coron, J.-S., Großschädl, J., Vadnala, P.K.: Secure conversion between boolean and arithmetic masking of any order. In: Batina, L., Robshaw, M. (eds.) CHES 2014. LNCS, vol. 8731, pp. 188–205. Springer, Heidelberg (2014)
4.
Coron, J.-S., Tchulkine, A.: A new algorithm for switching from arithmetic to boolean masking. In: Walter, C.D., Koç, Ç.K., Paar, C. (eds.) CHES 2003. LNCS, vol. 2779, pp. 89–97. Springer, Heidelberg (2003) CrossRef
5.
Debraize, B.: Efficient and provably secure methods for switching from arithmetic to boolean masking. In: Prouff, E., Schaumont, P. (eds.) CHES 2012. LNCS, vol. 7428, pp. 107–121. Springer, Heidelberg (2012) CrossRef
6.
Goubin, L.: A sound method for switching between boolean and arithmetic masking. In: Koç, Ç.K., Naccache, D., Paar, C. (eds.) CHES 2001. LNCS, vol. 2162, pp. 3–15. Springer, Heidelberg (2001) CrossRef
7.
Karroumi, M., Richard, B., Joye, M.: Addition with blinded operands. In: Prouff, E. (ed.) COSADE 2014. LNCS, vol. 8622, pp. 41–55. Springer, Heidelberg (2014)
8.
Kocher, P.C., Jaffe, J., Jun, B.: Differential power analysis. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 388–397. Springer, Heidelberg (1999)
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Mangard, S., Oswald, E., Popp, T.: Power Analysis Attacks - Revealing the Secrets of Smart Cards. Springer, New York (2007)
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Neiße, O., Pulkus, J.: Switching blindings with a view towards IDEA. In: Joye, M., Quisquater, J.-J. (eds.) CHES 2004. LNCS, vol. 3156, pp. 230–239. Springer, Heidelberg (2004) CrossRef
11.
Oswald, E., Mangard, S., Herbst, C., Tillich, S.: Practical second-order DPA attacks for masked smart card implementations of block ciphers. In: Pointcheval, D. (ed.) CT-RSA 2006. LNCS, vol. 3860, pp. 192–207. Springer, Heidelberg (2006) CrossRef
12.
Rivain, M., Dottax, E., Prouff, E.: Block ciphers implementations provably secure against second order side channel analysis. In: Nyberg, K. (ed.) FSE 2008. LNCS, vol. 5086, pp. 127–143. Springer, Heidelberg (2008) CrossRef
13.
Vadnala, P.K., Großschädl, J.: Algorithms for switching between boolean and arithmetic masking of second order. In: Gierlichs, B., Guilley, S., Mukhopadhyay, D. (eds.) SPACE 2013. LNCS, vol. 8204, pp. 95–110. Springer, Heidelberg (2013) CrossRef
Metadata
Title
Faster Mask Conversion with Lookup Tables
Authors
Praveen Kumar Vadnala
Johann Großschädl
Copyright Year
2015
Book
Constructive Side-Channel Analysis and Secure Design

Print ISBN: 978-3-319-21475-7

Electronic ISBN: 978-3-319-21476-4

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-21476-4_14

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