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On the Security of the (F)HMQV Protocol

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Progress in Cryptology – AFRICACRYPT 2016 (AFRICACRYPT 2016)

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Abstract

The HMQV protocol is under consideration for IEEE P1363 standardization. We provide a complementary analysis of the HMQV protocol. Namely, we point a Key Compromise Impersonation (KCI) attack showing that the two and three pass HMQV protocols cannot achieve their security goals. Next, we revisit the FHMQV building blocks, design and security arguments; we clarify the security and efficiency separation between HMQV and FHMQV, showing the advantages of FHMQV over HMQV.

A.P. Sarr—Partially supported by the CEA–MITIC.

P. Elbaz–Vincent—Partially supported by the LabEx PERSYVAL–Lab (ANR–11–LABX–0025–01).

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Notes

  1. 1.

    This is to date the best sieving algorithm for discrete logarithm over a prime field.

  2. 2.

    It takes few seconds on a i7–4790K to find such primes.

  3. 3.

    To launch this phase in the two–pass HMQV, the attacker has simply to wait, for instance, that \(\hat{B}\) uses the key to authenticate some value he/she knows.

  4. 4.

    Their abstract starts with “HMQV is one of the most efficient (provably secure) authenticated key–exchange protocols based on public–key cryptography, and is widely standardized.” To date, we are not aware of any standardization body which has already adopted the HMQV protocol.

  5. 5.

    These implementation approaches are not the only possible, however they seem to be common enough in real word to be considered in the model.

  6. 6.

    There is no dynamic key registration query in the eCK model [19]; the adversary is only allowed to select dishonest parties before starting its game. Dynamic key registration permits the adversary to select the parties it sets as dishonest after having seen their behaviour; this is an advantage for the adversary, and does not affect the comparability between the seCK and the eCK models.

  7. 7.

    Given the work [8], the Claim 1 from [21] about the formal incomparability between \(\text {CK}_\text {FHMQV}\) and the \(\text {CK}_\text {HMQV}\) models is trivial.

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Authors and Affiliations

  1. Laboratoire ACCA, Université Gaston Berger de Saint–Louis, Saint Louis, Senegal

    Augustin P. Sarr

  2. Institut Fourier – CNRS, Université Grenoble Alpes, Grenoble, France

    Philippe Elbaz–Vincent

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  1. Augustin P. Sarr
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  2. Philippe Elbaz–Vincent
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Correspondence to Augustin P. Sarr .

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  1. Ecole Normale Supérieure, Paris, France

    David Pointcheval

  2. University of Caen, Caen, France

    Abderrahmane Nitaj

  3. Al Akhawayn University in Ifrane, Ifrane, Morocco

    Tajjeeddine Rachidi

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Sarr, A.P., Elbaz–Vincent, P. (2016). On the Security of the (F)HMQV Protocol. In: Pointcheval, D., Nitaj, A., Rachidi, T. (eds) Progress in Cryptology – AFRICACRYPT 2016. AFRICACRYPT 2016. Lecture Notes in Computer Science(), vol 9646. Springer, Cham. https://doi.org/10.1007/978-3-319-31517-1_11

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