Cryptology ePrint Archive: Report 2021/819

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

Christof Beierle and Patrick Derbez and Gregor Leander and Gaëtan Leurent and Håvard Raddum and Yann Rotella and David Rupprecht and Lukas Stennes

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.

Category / Keywords: secret-key cryptography / GPRS Encryption, Stream Cipher, Algebraic attacks, GEA

Original Publication (in the same form): IACR-EUROCRYPT-2021

Date: received 15 Jun 2021

Contact author: christof beierle at rub de, patrick derbez at irisa fr, gregor leander at rub de, gaetan leurent at inria fr, haavardr at simula no, yann rotella at uvsq fr, david rupprecht at rub de, lukas stennes at rub de

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Version: 20210616:133848 (All versions of this report)

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