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36 Attacks on Rejsekortet 3.2.6.2 Time/memory-tradeoff in the TCCP The TCCP (Travel Card Customer Profile) is another good candidate for a precomputation attack. TCCP’s advantace over the TCCI is that its mutable fields are user-controllable, abusing the inherent feature of MACs that the plaintext is likely choosable. The precise contents of the section can be looked up in [5], but listed here are the user-mutable fields: • The passenger class • Preferred language • Dialogue preferences The other fields are other fields relating to the user, such as his/her birthday, etc. Conducting a pre-computation attack from the TCCP is likely more effective than the one described for the TCCI, because the user has complete control over the state of the sector. This entails that an attacker will be able to force a recalculation of the MAC, which can then be looked up in the table. 3.2.7 A practical time-memory trade-off against Rejsekortet As stated in 3.2.4.2 it is possible to get 64 bits of independent MAC data for some key if some field can be controlled into four different mutations. As was just established, the TCCP constitutes such a field. The preferred language can be expected to have at least two different values, Danish and English, and so does the passenger class, business class and economic class. This gives four different states that all have different MACs for some key, see table 3.1. The 16-bit MACs can be concatenated to form a 64-bit MAC. However, the key length for DES is 56, so the new 64-bit MAC can be shortened to 56 bits, giving a {0, 1} 56 → {0, 1} 56 mapping. It is now possible to construct a rainbow table mapping DES keys to this new 56- bit MAC. As described in section 3.2.5 this rainbow table will have the expected size of 2.2 TB if it is optimized equally for space efficiency and on-line key recovery time efficiency. However, values can be adjusted as the attacker sees fit. The step function f i for the ith column in the rainbow table is defined as shown in Figure 3.8.
3.2 Attacking the MAC 37 in f i 64b c 1 c 2 c 3 c 4 MAC MAC MAC MAC 64b cut cut cut cut 16b concatenation 64b cut 56b ⊕ i out Figure 3.8: The step function f i for the ith column of the rainbow table. The top to the concatenation function is the MAC-function, and the cut and XOR functions comprise the reduction function.
Page 1 and 2: Cryptanalysis of Rejsekortet Jens C
Page 3: 3 Abstract. This bachelor thesis an
Page 7: Resumé Denne bachelorafhandling er
Page 10 and 11: vi Glossary Rejsekort(et) Danish fo
Page 12 and 13: viii
Page 14 and 15: x CONTENTS 4.3 Other improvements .
Page 16 and 17: 2 On Rejsekortet Disclaimer: This r
Page 18 and 19: 4 On Rejsekortet are even capable o
Page 20 and 21: 6 On Rejsekortet 1.2.3 Mifare Mifar
Page 22 and 23: 8 On Rejsekortet 1. Reader sends a
Page 24 and 25: 10 On Rejsekortet Time of transacti
Page 26 and 27: 12 On Rejsekortet Figure 1.3: The C
Page 28 and 29: 14 On Rejsekortet 1.3.2.1 CBC-MAC C
Page 30 and 31: 16 On Rejsekortet
Page 32 and 33: 18 Security analysis and threat mod
Page 38 and 39: 24 Attacks on Rejsekortet 3.1 Rollb
Page 40 and 41: 26 Attacks on Rejsekortet 3.2 Attac
Page 42 and 43: 28 Attacks on Rejsekortet and cumbe
Page 44 and 45: 30 Attacks on Rejsekortet hash valu
Page 46 and 47: 32 Attacks on Rejsekortet 3.2.4 Int
Page 48 and 49: 34 Attacks on Rejsekortet 3.2.5 App
Page 52 and 53: 38 Attacks on Rejsekortet Language
Page 54 and 55: 40 Attacks on Rejsekortet It is not
Page 56 and 57: 42 Attacks on Rejsekortet specifica
Page 58 and 59: 44 Attacks on Rejsekortet might pro
Page 60 and 61: 46 Attacks on Rejsekortet that the
Page 62 and 63: 48 Attacks on Rejsekortet
Page 64 and 65: 50 Improvements 4.1.1 New MAC algor
Page 66 and 67: 52 Improvements functions tend to b
Page 68 and 69: 54 Improvements
Page 70 and 71: 56 Conclusion of the pre-computatio
Page 72 and 73: 58 Related research Sector 04 - UNK
Page 74 and 75: 60 Mail correspondence enquire abou
Page 76 and 77: 62 Mail correspondence * Kodningspr
Page 78 and 79: 64 Mail correspondence Som ingeniø
Page 80: 66 BIBLIOGRAPHY [9] Philippe Oechsl

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