Abstract. This contribution presents a new approach to optimize the efficiency of differential side channel cryptanalysis against block ciphers by advanced stochastic methods. We approximate the real leakage function within a suitable vector subspace. Under appropriate conditions profiling requires only one test key. For the key extraction we present a 'minimum principle' that solely uses deterministic data dependencies and the 'maximum likelihood principle' that additionally incorporates the characterization of the noise revealed during profiling. The theoretical predictions are accompanied and confirmed by experiments. We demonstrate that the adaptation of probability densities is clearly advantageous regarding the correlation method, especially, if multiple leakage signals at different times can be jointly evaluated. Though our efficiency at key extraction is limited by template attacks profiling is much more efficient which is highly relevant if the designer of a cryptosystem is bounded by the number of measurements in the profiling step.

Abstract. We introduce a new type of timing attack which enables the factorization of an RSA-modulus if the exponentiation with the secret exponent uses the Chinese Remainder Theorem and Montgomery's algorithm. Its standard variant assumes that both exponentiations are carried out with a simple square and multiply algorithm. However, although its efficiency decreases, our attack can also be adapted to more advanced exponentiation algorithms. The previously known timing attacks do not work if the Chinese Remainder Theorem is used.

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MicroArchitectural Analysis (MA) techniques, more specifically Simple Branch Prediction Analysis (SBPA) and Instruction Cache Analysis, have the potential of disclosing the entire execution flow of a software-implemented cryptosystem ([5,2]). In this paper we will show that one can completely break RSA in the original unpatched OpenSSL version (v.0.9.8e) even if the most secure configuration is in place, including all countermeasures against side-channel and MicroArchitectural analysis (in particular, base blinding). We also discuss (known) countermeasures that prevent this attack.In a first step we apply an instruction cache attack to reveal which Montgomery operations require extra reductions. To exploit this information we model the timing behavior of the modular exponentiation algorithm by a stochastic process. Its analysis provides the optimal guessing strategy, which reveals the secret key (mod p1) and finally the factorization of the RSA modulus n = p1p2. For the instruction cache attack we applied a spy process that was embedded in the target process (OpenSSL), which clearly facilitates the experimental part. This simplification yet does not nullify our results since in cache attacks empirical results from embedded spy processes and (suitably implemented) standalone spy processes are very close to each other [16] and, moreover, our guessing strategy is fault-tolerant. Interestingly, the second step of our attack is related to that of a particular combined power and timing attack on smart cards [23] (see also [27,22]).Before we published our result [1] we informed the OpenSSL development team who included a patch into the stable branch of v.0.9.7e ([31,32]) and CERT which informed software vendors ([33,34,35]). In particular, this countermeasure is included in the current version 0.9.8f. We have only analyzed OpenSSL, thus we currently do not know the strength of other cryptographic libraries.