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On the Correctness of Security Proofs for the 3GPP Confidentiality and Integrity Algorithms
Tetsu IWATA Kaoru KUROSAWA
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E87A
No.5
pp.11101118 Publication Date: 2004/05/01 Online ISSN:
DOI: Print ISSN: 09168508 Type of Manuscript: Special Section LETTER (Special Section on Discrete Mathematics and Its Applications) Category: Keyword: cryptography, f 8, f 9, modes of operation, provable security, block cipher, pseudorandom permutation,
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Summary:
f 8 and f 9 are standardized by 3GPP to provide confidentiality and integrity, respectively. It was claimed that f 8 and f 9 are secure if the underlying block cipher is a PseudoRandom Permutation (PRP), where f 9 is a slightly modified version of f 9. In this paper, however, we disprove both claims by showing a counterexample. We first construct a PRP F with the following property: There is a nonzero constant Cst such that for any key K, F_{K}()=(). We then show that f 8 and f 9 are completely insecure if F is used as the underlying block cipher. Therefore, PRP assumption does not necessarily imply the security of f 8 and f 9, and it is impossible to prove their security under PRP assumption. It should be stressed that these results do not imply the original f 8 and f 9 (with KASUMI as the underlying block cipher) are insecure, or broken. They simply undermine their provable security.


