Brier E., Peyrin T. (2010) A Forward-Secure Symmetric-Key Derivation Protocol. In: Abe M. (eds) Advances in Cryptology - ASIACRYPT 2010. ASIACRYPT 2010. Lecture Notes in Computer Science, vol 6477. Springer, Berlin, Heidelberg
In this article, we study an interesting and very practical key management problem. A server shares a symmetric key with a client, whose memory is limited to R key registers. The client would like to send private messages using each time a new key derived from the original shared secret and identified with a public string sent together with the message. The server can only process N computations in order to retrieve the derived key corresponding to a given message. Finally, the algorithm must be forward-secure on the client side: even if the entire memory of the client has leaked, it should be impossible for an attacker to retrieve previously used communication keys. Given N and R, the total amount T of keys the system can handle should be as big as possible.
In practice such a forward-secure symmetric-key derivation protocol is very relevant, in particular in the payment industry where the clients are memory-constraint paying terminals and where distributing symmetric keys on field is a costly process. At the present time, one standard is widely deployed: the Derive Unique Key Per Transaction (DUKPT) scheme defined in ANSI X9.24. However, this algorithm is complicated to apprehend, not scalable and offers poor performances.
We provide here a new construction, Optimal-DUKPT (or O-DUKPT), that is not only simpler and more scalable, but also more efficient both in terms of client memory requirements and server computations when the total number of keys T is fixed. Finally, we also prove that our algorithm is optimal in regards to the client memory R / server computations N / number of keys T the system can handle.