Back-End

Server

Figure 1.2: An RFID System composed of a set of RFID tags communicating wirelessly with a reader that is in itself connected to a back-end database server.

proposals for RFID tags, namely, the authentication protocol HB and the message authentication code S UASH. Concretely, we exhibit cryptographic attacks that enable an attacker to recover the tag’s secret key. e second part of the dissertation is then dedicated to assess the need of a privacy model. We contribute to this edi ce by proposing a privacy model for RFID tags that admits several levels depending on the needs of the application and the type of tags used in it.

1.1The Need for Dedicated Cryptographic Primitives for RFID Tags

To ensure the protection of an RFID system, the rst thing to do is to look back in the literature of cryptographic primitives and protocols and test whether any of the already proposed solutions can be applied. Unfortunately, it turns out that implementing classical algorithms is farbeyondthecapabilitiesofmostencounteredtypesofRFIDtags. estandardunitofmeasure for this capability is the Gate Equivalent (GE). e Gate Equivalent is a unit of measure which allows to specify manufacturing-technology-independent complexity of digital electronic circuits. In today’s Complementary metal–oxide–semiconductor (CMOS) technology, one GE refers to (the area taken by) one NAND Gate with two inputs and one output. For example, the circuit implementing the boolean function a ^ b needs 2 NAND gates, one for NAND and one for boolean inversion, and therefore costs 2 GE. For low-end RFID tags, it is commonly agreed that no more than 2 000 GE can be dedicated to security [JW a]. However, to date, the best implementation of the Advanced Encryption Standard (AES) needs 3 600 GE[FDW ], whichcanbereducedto 3 100 GEinanencryption-only architecture [HAHH ]. Similarily, a variant of the Digital Encryption Standard (DES), in which all S-boxes are identical, can be implemented within 1 848 GE [LPPS ]. On another hand, currently deployed hash functions proved too heavy to be considered for RFID tags [FR ]. For instance, having SHAon an RFID chip requires 8 120 GE, SHArequires 10 868 GE, MD demands 7 350 GE, and MD ts in 8 400 GE. In a recent work, Hutter, Feldhofer, and

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Wolkerstorfer [HFW ] achieved an implementation of AES and SHArestricted to - bit messages for a processor dedicated to producing ECDSA signatures in 2 387 GE. Concerning stream ciphers, the eStream portfolio for hardware oriented ciphers, currently consisting of the two ciphers MICKEY [BD a] and Trivium [CP ] require approximatively 3 400 GE and 2 300 GE respectively (we do not include G [HJMM ] in the list since it was broken by Dinur and Shamir [DS ]). While we are not aware of any cryptanalysis result on MICKEY, Trivium has been able to resist Dinur and Shamir’s cube attack [DS ].

Having said that, implementing public-key cryptography is an even greater challenge. Two di erent directions were taken in this line of research. On one side, elliptic curve cryptography was shown to be feasible on an RFID tag, although it requires more than 10 000 GE to be implemented [HWF ]. Similar results were obtained for hyperelliptic curve cryptography using approximatively 14 500 GE [FBV ]. On the other side, the lattice-based NTRU public-key encryption scheme [HPS ] can have its encryption algorithm implemented in 2 800 GE [ABF+ ]. A di erent approach was taken by Calmels, Canard, Girault, and Sibert [CCGS ]. In an e ort to circumvent the issue of the cost of implementing modular arithmetic in hardware, they proposed to adapt the GPS identi cation scheme [GPS ] by loading the tag with a set of precomputed data, called coupons. is trick allowed them to reduce the amount of operations a tag needs to carry out for authentication to a small number of arithmetic additions. However, besides needing a large memory to retain all the coupons, the GPS-with-coupon scheme is susceptible to availability issues and vulnerable against Denial of Service (DoS) attacks (Calmels et al.’s proof of concept used 2 600 GE for security and stored eight coupons that would be used for eight authentications).

e shortcomings of classical cryptographic primitives to meet the needs of RFIDs led to the rise of new proposals with innovative designs. Among those proposals, we mention the block ciphers KATAN and KTANTAN [CDK ] which can be implemented in less than 800 GE. Another interesting proposal was made by Guo, Peyrin, and Poschman who simplied the AES design to propose a block cipher, called a L [GPPR ], and a one-way hash function, called P [GPP ] that can t in less than 1 000 GE. Other proposals include the hash functions uark [AHMNP ] and S [BKL+ ]. However, relying on simpli ed designs is error prone as the con dence in the security of several newly proposed primitives is put under question. at was the case for schemes such as P [BKL+ ] for which the most recently published cryptanalysis succeeds in performing a key recovery attack on reduced rounds of the cipher [CS , KCS ], and PRINTcipher, a block cipher proposed in [KLPR ] and fully cryptanalyzed in [LAAZ ]

Inthe rstpartofthisthesis, weanalyzethesecurityoftwoofthemostinnovativeproposals for RFID tags, namely, HB [GRS b] and S UASH [Sha , Sha ].

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who succeeds in recovering the parties’ shared secret. Our attack is practical as the adversary only needs to trigger 220 or 235 protocol sessions, depending on the parameter set by Gilbert et al. proposed. We further study possible xes of the protocol, such as limiting the number of errors the problem is putting in its answers, but it turns out that even these variants do not stand against other variants of the attack. ese results were published at AsiaCrypt[OOV ].

Regarding the structure, we divided this analysis into two chapters. In Chapter , we give a more detailled presentation of the LPN problem and its properties. We also present the main protocols of the HB protocols, namely HB and HB+. We leave HB and its security analysis to Chapter .

. . From Public-Key Cryptography to MACs: e SQUASH Proposal

Another proposal we study is rather unusual as it builds a symmetric-key cryptographic primitive, a MAC, from a function that represents the core of one of the oldest and most studied

at least the same level of security Rabin’s scheme provides as it consists of encrypting a mixing

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