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ACM.bbl
\begin{thebibliography}{10}

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\newblock New directions in cryptography.
\newblock {\em IEEE Transactions on Information Theory}, IT-22(6):644--654,
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\bibitem{joux00one}
Antoine Joux.
\newblock A one round protocol for tripartite {D}iffie-{H}ellman.
\newblock In {\em ANTS-IV: Proceedings of the 4th International Symposium on
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\bibitem{rafaeli03survey}
Sandro Rafaeli and David Hutchison.
\newblock A survey of key management for secure group communication.
\newblock {\em ACM Comput. Surv.}, 35(3):309--329, 2003.

\bibitem{zou05secure}
Xukai Zou, Byrav Ramamurthy, and Spyros~S. Magliveras.
\newblock {\em Secure Group Communications Over Data Networks}.
\newblock Springer, New York, NY, USA, 2005.

\bibitem{steiner98cliques}
Michael Steiner, Gene Tsudik, and Michael Waidner.
\newblock {CLIQUES}: {A} new approach to group key agreement.
\newblock In {\em Proceedings of the 18th International Conference on
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\bibitem{rabi97observation}
Muhammad Rabi and Alan~T. Sherman.
\newblock An observation on associative one-way functions in complexity theory.
\newblock {\em Inf. Process. Lett.}, 64(5):239--244, 1997.

\bibitem{boneh02applications}
Dan Boneh and Alice Silverberg.
\newblock Applications of multilinear forms to cryptography.
\newblock Cryptology ePrint Archive, Report 2002/080, 2002.

\bibitem{Sherman:1986:CVT}
Alan~T. Sherman.
\newblock {\em Cryptology and {VLSI} (a two-part dissertation). {I}, {II},
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\newblock Thesis ({Ph.D.}), Laboratory for Computer Science, Massachusetts
  Institute of Technology, Cambridge, MA, USA, October 1986.
\newblock Supervised by Ronald Linn Rivest.

\bibitem{KaliksiRiSh88}
Burton~S. {Kaliksi, Jr.}, Ronald~L. Rivest, and Alan~T. Sherman.
\newblock Is the {D}ata {E}ncryption {S}tandard a group?
\newblock {\em Journal of Cryptology}, 1(1):3--36, 1988.

\bibitem{rabi93associative}
M.~Rabi and A.~Sherman.
\newblock Associative one-way functions: {A} new paradigm for secret-key
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\newblock Technical Report CS-TR-3183/UMIACS-TR-93-124, 1993.

\bibitem{homan00low}
Christopher~M. Homan.
\newblock Low ambiguity in strong, total, associative, one-way functions, 2000.

\bibitem{beygelzimer99oneway}
Alina Beygelzimer, Lance~A. Hemaspaandra, Christopher~M. Homan, and J{\"o}rg
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\newblock One-way functions in worst-case cryptography: Algebraic and security
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\newblock Technical Report TR722, 1999.

\bibitem{lane99creating}
Lane~A. Hemaspaandra and J\"{o}rg Rothe.
\newblock Creating strong, total, commutative, associative one-way functions
  from any one-way function in complexity theory.
\newblock {\em J. Comput. Syst. Sci.}, 58(3):648--659, 1999.

\bibitem{lane05enforcing}
Lane~A. Hemaspaandra, J\"{o}rg Rothe, and Amitabh Saxena.
\newblock Enforcing and defying associativity, commutativity, totality, and
  strong noninvertibility for one-way functions in complexity theory.
\newblock In {\em ICTCS}, 2005.

\bibitem{thesis03susan}
Susan Hohenberger.
\newblock The cryptographic impact of groups with infeasible inversion.
\newblock Master's thesis, Massachusetts Institute of Technology, 2003.
\newblock Advisor: Ronald L. Rivest.

\bibitem{saxena05novel}
Amitabh Saxena and Ben Soh.
\newblock A novel method for authenticating mobile agents with one-way
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\newblock In {\em Proceedings of The 7th International Symposium on Autonomous
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\bibitem{lane01if}
Lane~A. Hemaspaandra, Kari Pasanen, and J\"{o}rg Rothe.
\newblock If \emph{P} $\neq$ \emph{NP} then some strongly noninvertible
  functions are invertible.
\newblock In {\em FCT '01: Proceedings of the 13th International Symposium on
  Fundamentals of Computation Theory}, pages 162--171. Springer-Verlag, 2001.

\bibitem{Maurer99}
Ueli Maurer.
\newblock Information-theoretic cryptography.
\newblock In Michael Wiener, editor, {\em Advances in Cryptology --- CRYPTO
  '99}, volume 1666 of {\em Lecture Notes in Computer Science}, pages 47--64.
  Springer-Verlag, August 1999.

\bibitem{DBLP:conf/crypto/Chaum82}
David Chaum.
\newblock Blind signatures for untraceable payments.
\newblock In {\em CRYPTO'82}, pages 199--203, 1982.

\bibitem{babai84on}
L\'{a}szl\'{o} Babai and Endre Szemer\'{e}di.
\newblock On the complexity of matrix group problems {I}.
\newblock In {\em {FOCS}'1984}, pages 229--240, 1984.

\bibitem{rivest04notion}
Ronald~L. Rivest.
\newblock On the notion of pseudo-free groups.
\newblock In Moni Naor, editor, {\em TCC}, volume 2951 of {\em Lecture Notes in
  Computer Science}, pages 505--521. Springer, 2004.

\bibitem{boneh01short}
Dan Boneh, Ben Lynn, and Hovav Shacham.
\newblock Short signatures from the {W}eil pairing.
\newblock In {\em ASIACRYPT '01: Proceedings of the 7th International
  Conference on the Theory and Application of Cryptology and Information
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\bibitem{boneh01identitybased}
Dan Boneh and Matthew~K. Franklin.
\newblock Identity-based encryption from the {W}eil pairing.
\newblock {\em SIAM J. Comput.}, 32(3):586--615, 2003.

\bibitem{paulo02efficient}
Paulo S. L.~M. Barreto, Hae~Yong Kim, Ben Lynn, and Michael Scott.
\newblock Efficient algorithms for pairing-based cryptosystems.
\newblock In {\em CRYPTO '02: Proceedings of the 22nd Annual International
  Cryptology Conference on Advances in Cryptology}, pages 354--368, London, UK,
  2002. Springer-Verlag.

\bibitem{menzes96handbook}
Alfred~J. Menezes, Scott~A. Vanstone, and Paul C.~Van Oorschot.
\newblock {\em Handbook of Applied Cryptography}.
\newblock CRC Press, Inc., Boca Raton, FL, USA, 1996.

\bibitem{joux01separating}
Antoine Joux and Kim Nguyen.
\newblock Separating {D}ecision {D}iffie-{H}ellman from {D}iffie-{H}ellman in
  cryptographic groups.
\newblock Technical Report 2001/003, 2001.

\bibitem{koblitz87course}
Neal Koblitz.
\newblock {\em A course in number theory and cryptography}.
\newblock Springer-Verlag New York, Inc., New York, NY, USA, 1987.

\bibitem{DBLP:conf/tcc/BonehGN05}
Dan Boneh, Eu-Jin Goh, and Kobbi Nissim.
\newblock Evaluating {2-DNF} formulas on ciphertexts.
\newblock In Joe Kilian, editor, {\em TCC}, volume 3378 of {\em Lecture Notes
  in Computer Science}, pages 325--341. Springer, 2005.

\bibitem{DBLP:conf/eurocrypt/Paillier99}
Pascal Paillier.
\newblock Public-key cryptosystems based on composite degree residuosity
  classes.
\newblock In {\em EUROCRYPT}, pages 223--238, 1999.

\bibitem{rivest78method}
R.~L. Rivest, A.~Shamir, and L.~Adleman.
\newblock A method for obtaining digital signatures and public-key
  cryptosystems.
\newblock {\em Commun. ACM}, 21(2):120--126, 1978.

\bibitem{889813}
M.~O. Rabin.
\newblock Digitalized signatures and public-key functions as intractable as
  factorization.
\newblock Technical report, Massachusetts Institute of Technology, Cambridge,
  MA, USA, 1979.

\bibitem{catalano01bit}
Dario Catalano, Rosario Gennaro, and Nick Howgrave-Graham.
\newblock The bit security of {P}aillier's encryption scheme and its
  applications.
\newblock In {\em EUROCRYPT '01: Proceedings of the International Conference on
  the Theory and Application of Cryptographic Techniques}, pages 229--243,
  London, UK, 2001. Springer-Verlag.

\bibitem{catalano02pailliers}
D.~Catalano, R.~Gennaro, and N.~H. Graham.
\newblock Paillier's trapdoor function hides up to {O}(n) bits.
\newblock {\em Journal of Cryptology}, 15(4):251--269, 2002.

\bibitem{rivest01how}
Ronald~L. Rivest, Adi Shamir, and Yael Tauman.
\newblock How to leak a secret.
\newblock {\em Lecture Notes in Computer Science}, 2248:552--??, 2001.

\bibitem{fiat94broadcast}
Amos Fiat and Moni Naor.
\newblock Broadcast encryption.
\newblock {\em Lecture Notes in Computer Science}, 773:480--??, 1994.

\bibitem{DBLP:conf/eurocrypt/ChabannePP05}
Herv{\'e} Chabanne, Duong~Hieu Phan, and David Pointcheval.
\newblock Public traceability in traitor tracing schemes.
\newblock In Ronald Cramer, editor, {\em EUROCRYPT}, volume 3494 of {\em
  Lecture Notes in Computer Science}, pages 542--558. Springer, 2005.

\bibitem{fujisaki99secure}
Eiichiro Fujisaki and Tatsuaki Okamoto.
\newblock Secure integration of asymmetric and symmetric encryption schemes.
\newblock {\em Lecture Notes in Computer Science}, 1666:537--554, 1999.

\bibitem{DBLP:conf/asiacrypt/KimLL04}
Hyun-Jeong Kim, Su-Mi Lee, and Dong~Hoon Lee.
\newblock Constant-round authenticated group key exchange for dynamic groups.
\newblock In Pil~Joong Lee, editor, {\em ASIACRYPT}, volume 3329 of {\em
  Lecture Notes in Computer Science}, pages 245--259. Springer, 2004.

\bibitem{bresson03mutual}
E.~Bresson, O.~Chevassut, A.~Essiari, and D.~Pointcheval.
\newblock Mutual authentication and group key agreement for low-power mobile
  devices, 2003.

\bibitem{cryptoeprint:2004:251}
Junghyun Nam, Seungjoo Kim, and Dongho Won.
\newblock Attacks on {B}resson-{C}hevassut-{E}ssiari-{P}ointcheval's group key
  agreement scheme for low-power mobile devices.
\newblock Cryptology ePrint Archive, Report 2004/251, 2004.

\end{thebibliography}
