A Concrete Block Cipher Realization Based on SRAM-PRFs

In Sect.7.3it was shown how a secure block cipher can be constructed using n-to-n bit PUF-wPRFs. However, when using SRAM PUFs, constructing a PUF-wPRF with a reasonably large input size n is infeasible. Here, we construct a block cipher with the practically feasible expanding SRAM-PRF. As an example, we discuss an expanding Luby–Rackoff cipher. The security of such schemes was studied in [40]

and lower bounds on the number of rounds were given. We present details of a SRAM-PRF construction taking an 8-bit challenge as input and producing a 120-bit extracted output. As an instantiation for the PUF, we take an SRAM PUF with an assumed average bit-error probability of 15% and an estimated min-entropy content of 0.95 bit/cell, which are realistic values according to the experimental observations in [22]. We use a TMV-threshold of(NT =99,pT =10⁻⁹), yielding a safe very low average error probability using a practically feasible number of votes. Simula-tions and experiments on the SRAM PUF show that about 30% of the SRAM cells produce a dark bit with respect to this TMV-threshold. The strong extractor only has to compress by a factor of _0.¹₉₅, accounting for the limited min-entropy in the PUF response. An SRAM PUF containing at least _0.¹₉₅ · ²_70%^8·120bits=5.6 KB of SRAM cells is needed to build this PUF-wPRF.

We determine the parameters for a proof-of-concept construction using the lower bound of rounds derived in [40]. Observe that this does not automatically imply the security of the scheme but shows a lower bound on the implementation size.

• We construct a block cipher with block length 128.

• In every round, an expanding SRAM-PRF:{0,1}⁸ → {0,1}¹²⁰is used. Such a SRAM-PRF uses about 5.6 KB of SRAM cells, as shown earlier. The PUF-wPRF is operated in all-at-once mode.

• The results from [40] suggest to use at least 48 rounds, each with a different PUF-wPRF.

• The entire block cipher uses 48·5.6 KB≈271 KB of SRAM cells. The helper tables also require 5.6 KB each.

Implementing 48 SRAM PUFs using a total of 271 KB of SRAM cells is feasible on recent ICs, and 48 rounds can be evaluated relatively fast. Storing and loading 48 helper tables of 5.6 KB each is also achievable in practice. Observe that the size depends linearly on the number of rounds. The according parameters for more rounds can be easily derived. Reducing the input size of the SRAM-PRF will yield an even smaller amount of needed SRAM cells and smaller helper tables, but the number of rounds will increase. A time-area tradeoff is hence possible.

9 Conclusions

In this chapter we propose a leakage-resilient encryption scheme that makes use of physically unclonable functions (PUFs). The core component is a new PUF-based cryptographic primitive, termed PUF-PRF, that is similar to a pseudorandom func-tion (PRF). We showed that PUF-PRFs possess cryptographically useful algorith-mic and physical properties that come from the random character of their physical structures.

Of course, any physical model can only approximately describe real life.

Although experiments support our model for the considered PUF implementations, more analysis is necessary. In this context it would be interesting to consider other types of PUFs which fit into our model or might be used for other cryptographic applications. Furthermore, a natural continuation of this works would be to explore other cryptographic schemes based on PUF-PRFs, e.g., hash functions or public-key encryption.

Acknowledgments We thank Stefan Lucks for useful comments and discussions. The work of Berk Sunar was supported by the National Science Foundation Cybertrust grant No. CNS-0831416.

The work of Roel Maes is funded by IWT-Flanders grant No. 71369 and is in part supported by the IAP Program P6/26 BCRYPT of the Belgian State and K.U.Leuven BOF funding (OT/06/04).

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