Password-authenticated key agreement

In cryptography, a password-authenticated key agreement method is an interactive method for two or more parties to establish cryptographic keys based on one or more party's knowledge of a password.

An important property is that an eavesdropper or man in the middle cannot obtain enough information to be able to brute force guess a password without further interactions with the parties for each (few) guesses. This means that strong security can be obtained using weak passwords.


Password-authenticated key agreement generally encompasses methods such as:

  • Balanced password-authenticated key exchange
  • Augmented password-authenticated key exchange
  • Password-authenticated key retrieval
  • Multi-server methods
  • Multi-party methods

In the most stringent password-only security models, there is no requirement for the user of the method to remember any secret or public data other than the password.

Password authenticated key exchange (PAKE) is where two or more parties, based only on their knowledge of a password, establish a cryptographic key using an exchange of messages, such that an unauthorized party (one who controls the communication channel but does not possess the password) cannot participate in the method and is constrained as much as possible from brute force guessing the password. (The optimal case yields exactly one guess per run exchange.) Two forms of PAKE are Balanced and Augmented methods.

Balanced PAKE allows parties that use the same password to negotiate and authenticate a shared key. Examples of these are:

Augmented PAKE is a variation applicable to client/server scenarios, in which the server does not store password-equivalent data. This means that an attacker that stole the server data still cannot masquerade as the client unless they first perform a brute force search for the password. Examples include:

  • AMP
  • Augmented-EKE
  • PAK-X[1]
  • SRP (Secure Remote Password protocol) -- designed to be not encumbered by patents.
  • AugPAKE (RFC 6628)
  • OPAQUE[6]
  • SPAKE2+[5]

Password-authenticated key retrieval is a process in which a client obtains a static key in a password-based negotiation with a server that knows data associated with the password, such as the Ford and Kaliski methods. In the most stringent setting, one party uses only a password in conjunction with N (two or more) servers to retrieve a static key. This is completed in a way that protects the password (and key) even if N-1 of the servers are completely compromised.

Brief history

The first successful password-authenticated key agreement methods were Encrypted Key Exchange methods described by Steven M. Bellovin and Michael Merritt in 1992. Although several of the first methods were flawed, the surviving and enhanced forms of EKE effectively amplify a shared password into a shared key, which can then be used for encryption and/or message authentication. The first provably-secure PAKE protocols were given in work by M. Bellare, D. Pointcheval, and P. Rogaway (Eurocrypt 2000) and V. Boyko, P. MacKenzie, and S. Patel (Eurocrypt 2000). These protocols were proven secure in the so-called random oracle model (or even stronger variants), and the first protocols proven secure under standard assumptions were those of O. Goldreich and Y. Lindell (Crypto 2001) which serves as a plausibility proof but is not efficient, and J. Katz, R. Ostrovsky, and M. Yung (Eurocrypt 2001) which is practical.

The first password-authenticated key retrieval methods were described by Ford and Kaliski in 2000.

A considerable number of alternative, secure PAKE protocols were given in work by M. Bellare, D. Pointcheval, and P. Rogaway,variations, and security proofs have been proposed in this growing class of password-authenticated key agreement methods. Current standards for these methods include IETF RFC 2945, RFC 5054, RFC 5931, RFC 5998, RFC 6124, RFC 6617, RFC 6628 and RFC 6631, IEEE Std 1363.2-2008, ITU-T X.1035 and ISO-IEC 11770-4:2006.

See also


  1. Boyko, V.; P. MacKenzie; S. Patel (2000). Provably Secure Password-Authenticated Key Exchange Using Diffie-Hellman. Advances in Cryptology -- Eurocrypt 2000, LNCS. Lecture Notes in Computer Science. 1807. Springer-Verlag. pp. 156–171. doi:10.1007/3-540-45539-6_12. ISBN 978-3-540-67517-4.
  2. Wang, Yongge (2006). "Security Analysis of a Password-Based Authentication Protocol Proposed to IEEE 1363" (PDF). Theoretical Computer Science. 352 (1–3): 280–287. doi:10.1016/j.tcs.2005.11.038.
  4. Abdalla, M.; D. Pointcheval (2005). Simple Password-Based Encrypted Key Exchange Protocols (PDF). Topics in Cryptology – CT-RSA 2005. Lecture Notes in Computer Science. 3376. Springer Berlin Heidelberg. pp. 191–208. CiteSeerX doi:10.1007/978-3-540-30574-3_14. ISBN 978-3-540-24399-1.
  5. Ladd, Watson. Kaduk, Benjamin (ed.). "SPAKE2, a PAKE (Draft)". IETF.
  6. Krawczyk, Hugo. "The OPAQUE Asymmetric PAKE Protocol (Draft)". IETF.

Further reading

  • Bellare, M.; D. Pointcheval; P. Rogaway (2000). Authenticated Key Exchange Secure against Dictionary Attacks. Advances in Cryptology -- Eurocrypt 2000 LNCS. Lecture Notes in Computer Science. 1807. Springer-Verlag. pp. 139–155. doi:10.1007/3-540-45539-6_11. ISBN 978-3-540-67517-4.
  • Bellovin, S. M.; M. Merritt (May 1992). Encrypted Key Exchange: Password-Based Protocols Secure Against Dictionary Attacks. Proceedings of the I.E.E.E. Symposium on Research in Security and Privacy. Oakland. p. 72. doi:10.1109/RISP.1992.213269. ISBN 978-0-8186-2825-2.
  • Ford, W.; B. Kaliski (14–16 June 2000). Server-Assisted Generation of a Strong Secret from a Password. Proceedings of the IEEE 9th International Workshops on Enabling Technologies: Infrastructure for Collaborative Enterprises. Gaithersburg MD: NIST. p. 176. CiteSeerX doi:10.1109/ENABL.2000.883724. ISBN 978-0-7695-0798-9.
  • Goldreich, O.; Y. Lindell (2001). Session-Key Generation Using Human Passwords Only. Advances in Cryptology -- Crypto 2001 LNCS. Lecture Notes in Computer Science. 2139. Springer-Verlag. pp. 408–432. doi:10.1007/3-540-44647-8_24. ISBN 978-3-540-42456-7.
  • "IEEE Std 1363.2-2008: IEEE Standard Specifications for Password-Based Public-Key Cryptographic Techniques". IEEE. 2009. Cite journal requires |journal= (help)
  • Katz, J.; R. Ostrovsky; M. Yung (2001). "Efficient Password-Authenticated Key Exchange Using Human-Memorable Passwords". 2045. Springer-Vergal. Cite journal requires |journal= (help)
  • T. Wu. The SRP-3 Secure Remote Password Protocol. IETF RFC 2945.
  • D. Taylor, T. Wu, N. Mavrogiannopoulos, T. Perrin. Using the Secure Remote Password (SRP) Protocol for TLS Authentication. IETF RFC 5054.
  • D. Harkins, G.Zorn. Extensible Authentication Protocol (EAP) Authentication Using Only a Password. IETF RFC 5931.
  • Y. Sheffer, G. Zorn, H. Tschofenig, S. Fluhrer. An EAP Authentication Method Based on the Encrypted Key Exchange (EKE) Protocol. IETF RFC 6124.
  • D. Harkins. Secure Pre-Shared Key (PSK) Authentication for the Internet Key Exchange Protocol (IKE). IETF RFC 6617.
  • ISO/IEC 11770-4:2006 Information technology—Security techniques—Key management—Part 4: Mechanisms based on weak secrets.
  • "IEEE Std 802.11-2012: IEEE Standard for Information Technology-- Part 11 Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specification". IEEE. 2012. Cite journal requires |journal= (help)
  • Jarecki, Stanislaw; Krawczyk, Hugo; Xu, Jiayu (2018). OPAQUE: An Asymmetric PAKE Protocol Secure Against Pre-Computation Attacks (PDF). Advances in Cryptology. Lecture Notes in Computer Science. 10822. pp. 456–486. doi:10.1007/978-3-319-78372-7_15. ISBN 978-3-319-78371-0.
  • Smyshlyaev, Stanislav; Oshkin, Igor; Alekseev, Evgeniy; Ahmetzyanova, Liliya (2015). "On the Security of One Password Authenticated Key Exchange Protocol" (PDF). Cryptology ePrint Archive (Report 2015/1237).
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