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Practical and Robust Secure Logging from Fault-Tolerant Sequential Aggregate Signatures

Part of the Lecture Notes in Computer Science book series (LNSC,volume 10592)

Abstract

Keeping correct and informative log files is crucial for system maintenance, security and forensics. Cryptographic logging schemes offer integrity checks that protect a log file even in the case where an attacker has broken into the system.

A relatively recent feature of these schemes is resistance against truncations, i.e. the deletion and/or replacement of the end of the log file. This is especially relevant as system intruders are typically interested in manipulating the later log entries that point towards their attack. However, there are not many schemes that are resistant against truncating the log file. Those that are have at least one of the following disadvantages: They are memory intensive (they store at least one signature per log entry), or fragile (i.e. a single error in the log renders the signature invalid and useless in determining where the error occurred).

We obtain a publicly-verifiable secure logging scheme that is simultaneously robust, space-efficient and truncation secure with provable security under simple assumptions. Our generic construction uses forward-secure signatures, in a plain and a sequential aggregate variant, where the latter is additionally fault-tolerant, as recently formalized by Hartung et al. [9]. Fault-tolerant schemes can cope with a number of manipulated log entries (bounded a priori) and offer strong robustness guarantees while still retaining space efficiency. Our implementation and the accompanying performance measurements confirm the practicality of our scheme.

Keywords

  • Sequential Aggregate Signatures
  • Fault-Tolerance
  • Secure Logging
  • Truncation-Security
  • Forward-Security

G. Hartung—The project underlying this report was supported by the German Federal Ministry of Education and Research under Grant No. 01|S15035A. The responsibility for the contents of this publication lies with the author.

A. Koch, J. Koch and D. Hartmann—This work was supported by the German Federal Ministry of Education and Research within the framework of the project KASTEL_IoE in the Competence Center for Applied Security Technology (KASTEL).

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Notes

  1. 1.

    The terms “claim” and “claim sequence” are borrowed from [9]. However, we have added an epoch index i to each claim, because we are considering forward security in this work.

  2. 2.

    This security notion is slightly weaker with respect to the non-triviality of forgeries than the one for sequential aggregate signatures by Lysyanskaya et al. [19]. There, they allow for all messages in \(C^*\) to be already queried before, but in different order. However, our notion additionally considers forward security.

  3. 3.

    forward-secure existentially unforgeable under chosen log message attacks.

  4. 4.

    Remember that we assume that m and i can be uniquely derived from \(m \mathop {\Vert }i\), which implies that the claims and also differ after concatenating \(j'\) to their messages. Since \(j'\) is also only used once, the claim cannot become equal to any other claim of after this concatenation, either.

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Correspondence to Gunnar Hartung , Björn Kaidel , Alexander Koch or Jessica Koch .

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A Implementation Details

A Implementation Details

This section gives details about our implementation of the scheme from Sect. 4.1. Our implementation is written in C++11, and will be made available under a free software license. For the BM-FSS scheme, we chose a modulus size of 1024 bits, roughly equivalent to a security level of 80 bit. The BGLS scheme was instantiated using elliptic curve groups 160 bits, and the base field had 1024 bits. We used an instantiation of the cover-free family based on polynomials, described in [16]. For a CFF supporting \(n = 100\), 1000, and 10000 messages, we chose the field size \(q = 5\), 11, and 23, respectively, and fixed the polynomial degree at \(k = 2\). This led to \(d = 2, 5\) and 11, respectively. (The resulting CFFs were slightly larger than required: They supported 125, 1331, and 12167 messages, respectively.) Whenever a hash function was needed, we used SHA-256. We used a constant string of 200 bytes for all messages.

Our experiments were conducted on a laptop computer with an Intel Core i5-2430M CPU [12] with a clock rate of 2.4 GHz. (Our implementation is not parallelized and therefore did not make use of the additional processor cores.) The processor has private (per-core) caches of 128 KB (Level 1) and 512 KB (Level 2), and a shared Level 3 Cache of 3072 KB [11, Sect. 1.1] The system was equipped with 5.7 GiB of RAM and running a 64-bit version desktop version of the Fedora 23 GNU/Linux operating system, equipped with Linux Kernel version 4.4.9-300. All code was compiled with the GNU C Compiler (version 5.3.1) and optimization level set to -O2. We used Shoups NTL library [25] (version 9.4.0) for the implementation of the BM-FSS scheme and the PBC library [18] (version 0.5.14) for the implementation of the BGLS-FS-SAS scheme.

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Hartung, G., Kaidel, B., Koch, A., Koch, J., Hartmann, D. (2017). Practical and Robust Secure Logging from Fault-Tolerant Sequential Aggregate Signatures. In: Okamoto, T., Yu, Y., Au, M., Li, Y. (eds) Provable Security. ProvSec 2017. Lecture Notes in Computer Science(), vol 10592. Springer, Cham. https://doi.org/10.1007/978-3-319-68637-0_6

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