Advertisement

A Message Authentication Code Based on Unimodular Matrix Groups

  • Matthew Cary
  • Ramarathnam Venkatesan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2729)

Abstract

We present a new construction based on modular groups. A novel element of our construction is to embed each input into a sequence of matrices with determinant ±1, the product of which yields the desired mac. We analyze using the invertibility and the arithmetic properties of the determinants of certain types of matrices; this may be of interest in other applications. Performance results on our preliminary implementations show the speed of our mac is competitive with recent fast mac algorithms, achieving 0.5 Gigabytes per second on a 1.06 GHz Celeron.

Keywords

Message authentication efficient mac hash functions 

References

  1. [ALW01]
    Alon, N., Lubotzky, A., Wigderson, A.: Semi-direct product in groups and Zig-zag product in graphs: Connections and applications. In: FOCS 2001, pp. 630–637. IEEE, Los Alamitos (2001)Google Scholar
  2. [BCK96]
    Bellare, M., Canetti, R., Krawczyk, H.: Keying hash functions for message authentication. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 1–15. Springer, Heidelberg (1996)Google Scholar
  3. [Ber]
    Bernstein, D.: Floating-point arithmetic and message authentication. draft available as, http://cr.yp.to/papers/hash127.dvi
  4. [BHK+99]
    Black, J., Halevi, S., Krawczyk, H., Krovetz, T., Rogaway, P.: UMAC: Fast and secure message authentication. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 216–233. Springer, Heidelberg (1999)Google Scholar
  5. [BHK+00]
    Black, J., Halevi, S., Krawczyk, H., Krovetz, T., Rogaway, P.: UMAC home page (2000), http://www.cs.ucdavis.edu/~rogaway/umac
  6. [BKR00]
    Bellare, M., Kilian, J., Rogaway, P.: The security of the cipher block chaining message authentication code. Journal of Computer and System Sciences 61(3), 362–399 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  7. [CW81]
    Carter, W.: New hash functions and their use in authentication and set equality. Journal of Computer and System Sciences 22(3), 265–279 (1981)Google Scholar
  8. [Gol97]
    Golic, J.: Linear statistical weaknesses in alleged RC4 keystream generator. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 226–238. Springer, Heidelberg (1997)Google Scholar
  9. [HK97]
    Halevi, S., Krawczyk, H.: MMH: Software message authentication in the Gbit/second rates. In: Fast Software Encryption, pp. 172–189 (1997)Google Scholar
  10. [JV98]
    Jakubowski, M.H., Venkatesan, R.: The chain and sum primitive and its applications to MACs and stream ciphers. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 281–293. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  11. [KS]
    Klimov, A., Shamir, A.: A new class of invertible mappings. In: Crypto 2001, Rump Session (2001)Google Scholar
  12. [Mir02]
    Mironov, I.: Not so random shuffles of RC4. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, p. 304. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  13. [MvOV97]
    Menezes, A.J., Van Oorschot, P.C., Vanstone, S.A.: Handbook of Applied Cryptography. CRC Press, Boca Raton (1997)zbMATHGoogle Scholar
  14. [MT98]
    Mister, S., Tavares, S.E.: Cryptanalysis of RC4-like Cipher. In: Tavares, S., Meijer, H. (eds.) SAC 1998. LNCS, vol. 1556, pp. 131–143. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  15. [Rog99]
    Rogaway, P.: Bucket hashing and its application to fast message authentication. Journal of Cryptology: the Journal of the International Association for Cryptologic Research 12(2), 91–115 (1999)zbMATHMathSciNetGoogle Scholar
  16. [Sho96]
    Shoup, V.: On fast and provably secure message authentication based on universal hashing. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 313–328. Springer, Heidelberg (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Matthew Cary
    • 1
  • Ramarathnam Venkatesan
    • 2
  1. 1.University of Washington 
  2. 2.Microsoft Research 

Personalised recommendations