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Cryptanalysis of the GPRS Encryption Algorithms GEA-1 and GEA-2

Part of the Lecture Notes in Computer Science book series (LNSC,volume 12697)

Abstract

This paper presents the first publicly available cryptanalytic attacks on the GEA-1 and GEA-2 algorithms. Instead of providing full 64-bit security, we show that the initial state of GEA-1 can be recovered from as little as 65 bits of known keystream (with at least 24 bits coming from one frame) in time \(2^{40}\) GEA-1 evaluations and using 44.5 GiB of memory.

The attack on GEA-1 is based on an exceptional interaction of the deployed LFSRs and the key initialization, which is highly unlikely to occur by chance. This unusual pattern indicates that the weakness is intentionally hidden to limit the security level to 40 bit by design.

In contrast, for GEA-2 we did not discover the same intentional weakness. However, using a combination of algebraic techniques and list merging algorithms we are still able to break GEA-2 in time \(2^{45.1}\) GEA-2 evaluations. The main practical hurdle is the required knowledge of 1600 bytes of keystream.

Keywords

  • GPRS Encryption
  • Stream cipher
  • Algebraic attacks
  • GEA

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Notes

  1. 1.

    Available via https://www.legifrance.gouv.fr/jorf/id/JORFTEXT000000753702 and https://www.legifrance.gouv.fr/jorf/id/JORFTEXT000000753703, accessed Oct-06, 2020.

  2. 2.

    See minute 32:15 of the recorded talk.

  3. 3.

    The size of the registers are visible in the live state-recovery attack, see minute 48:25 of the recorded talk.

  4. 4.

    The authors acknowledged Mate Soos for ideas and also admitted that the live attack did not apply the SAT solver yet.

  5. 5.

    The complexity will be measured by the amount of operations that are roughly as complex as GEA-1 evaluations (for generating a keystream of size \(\le 128\) bit).

  6. 6.

    In a brute-force search, the initialization requires at least 195 clocking of the W register per key.

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Acknowledgment

This work was supported by the German Research Foundation (DFG) within the framework of the Excellence Strategy of the Federal Government and the States – EXC 2092 CaSa – 39078197, and by French Agence Nationale de la Recherche (ANR), under grant ANR-20-CE48-0017 (project SELECT). Patrick Derbez was supported by the French Agence Nationale de la Recherche through the CryptAudit project under Contract ANR-17-CE39-0003.

Most of all, we give thanks to Dieter Spaar and Harald Welte for their support and contact persons of the osmocom project.

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Correspondence to Christof Beierle , Patrick Derbez , Gregor Leander , Gaëtan Leurent , Håvard Raddum , Yann Rotella , David Rupprecht or Lukas Stennes .

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Appendices

Appendix A Source Code to Compute the Kernels

figure d

Appendix B Source Code to Compute the Dimensions

figure e

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Beierle, C. et al. (2021). Cryptanalysis of the GPRS Encryption Algorithms GEA-1 and GEA-2. In: Canteaut, A., Standaert, FX. (eds) Advances in Cryptology – EUROCRYPT 2021. EUROCRYPT 2021. Lecture Notes in Computer Science(), vol 12697. Springer, Cham. https://doi.org/10.1007/978-3-030-77886-6_6

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