Talk given at eSmart 2010. How to attack the Hitag2 cipher in RFID trannsponders

Courtois, NT

O'Neil, S

Quisquater, J-J

English

UCL Discovery

Practical Algebraic Attacks on the HITAG2TM Stream Cipher in RFID TranspondersNicolas T. Courtois 1Sean O’Neil 2 Jean-Jacques Quisquater 3 1  - University College London, UK2  - VEST Corporation, France3  - Université Catholique de Louvain, BelgiumAlgebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 2DisclaimerFirst of all, this pure crypto research:Spec of              Algebraicthe cipher  =>     Attack. Not all attacks work on actual industrial systems due to the protocol subtleties. Moreover: one should not expect that every information found on the Internet is correct. One can expect some small glitches…Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 3Outline1. Hitag2 cipher and products.2. Discussion: open source vs. closed source crypto.3. Algebraic attacks with SAT solvers.4. Our results. [Full paper published in ISC 2009, Pisa Italy, 7-9 September 2009, Springer LNCS]5. Industry impact, discussion.Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 4Hitag2• A stream cipher used in car locks [e.g. BMW]: Philips Hitag2 family. • Also used in building access.– According to [Nohl, Plotz HAR’09] used in German government and army buildings…– But Hitag2 proximity cards are not available anymore in shops. They have been discontinued.Here we concentrate just on car locks.Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 5What’s Inside?Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 6Open Source vs. Closed Source CryptoAlgebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 7Secrecy:Very frequently an obviousbusiness decision.• Creates entry barriers for competitors.• But also defends against hackers.Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 8Kerckhoffs’ principle: [1883]“The system must remain secure should it fall in enemy hands …”Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 9*Remark:Smart Cards:They are already in ‘enemy’ hands- even more for RFID…Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 10Kerckhoffs’ principle: [1883]Most of the time: incorrectly understood. No obligation to disclose.• Security when disclosed.• Better security when not disclosed???Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 11Yes (1,2,3):1. Military: layer the defences.Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 12Yes (2):2) Basic economics:these 3 extra months(and not more ￿)are simply worth a a lot of money.Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 13Yes (3):3) Prevent the erosion of profitability / barriers for entry for competitors / “inimitability”Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 14Kerckhoffs principle is kind of WRONGin the world of smart cardsReasons: • side channel attacks are HARD and COSTLY to prevent when the algo is known• in some applications, for example Pay TV the system is broken immediately when the cryptographic algorithms are public.Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 15Kerckhoffs principle is kind of WRONG?Well OK, but then we need other means to evaluate evaluate evaluate evaluate crypto algorithms used by the industry.• [OLD] private consulting…• [NEW] TODAY: Automated Cryptanalysis Automated Cryptanalysis Automated Cryptanalysis Automated CryptanalysisSpec of              Try ourthe cipher  =>     software Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 16Silicon HackingAlgebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 17Tarnovsky Lab [Freelance Silicon Hacker]Only a few thousands of dollars worth of equipmentAlgebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 18Clear and Present DangerReverse engineering is NOT that hard.No need for a FIB device (Focused Ion Beam, 0.5 M€).A few thousand dollars microscope  +software.Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 19Silicon Hacking => WikipediaTMAlgebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 20Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 21Crypto-1 is VERY WEAK• Crypto 1 Has regular LFSR taps =>Broken in 0.05 seconds. [de Koning Gans et al, Esorics 2008]Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 22much better:• • • Crypto 1 Has regular LFSR taps  Crypto 1 Has regular LFSR taps  Crypto 1 Has regular LFSR taps =>Broken in 0.05 seconds =>Broken in 0.05 seconds =>Broken in 0.05 seconds.  .  . [de [de [de Koning Gans Koning Gans Koning Gans et al, et al, et al, Esorics Esorics Esorics 2008] 2008] 2008]• Hitag 2 has IRREGULAR taps. Not so easy.• State of the art: Inversion attacks: – [Ross Anderson: Searching for the Optimum Correlation Attack, In FSE’94] – Our present work is a sort of automated inversion attack where human insights into how to invert the augmented filter function are replaced by the [clever] SAT solver software…Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 23Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 24Silicon Hacking => WikipediaA Cryptanalyst can start working…Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 25Exhaustive Key Search• 48 bits, about 4 years on 1 CPU. • But only hours/days with more expensive devices such as FPGA/Copacobana etc…Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 26Algebraic CryptanalysisAlgebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 27Algebraic Cryptanalysis [Shannon]Breaking a « good » cipher should require:“as much work as solving a system of simultaneous equations in a large number of unknowns of a complex type”[Shannon, 1949]Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 28Algebraic Cryptanalysis: An Emerging TechnologyAESXSLGartner’s Technology Hype CycleAlgebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 29Strong or Weak?High Algebraic Immunity.• Does NOT help. • Many “direct” algebraic attacks exist. We can break “any cipher”, if not too complex…Our fastest attacks use algebraic equations + conversion + SAT solvers • [cf. recent attacks on DES and KeeLoq by Courtois and Bard 2007-08]Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 30Our Attacks…AC can break “any cipher”, if not too complex…Remark: • Other attacks can be faster.• However, this method is more generally applicable: • we can also break many modified versions of Hitag2• and this without any human intervention !Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 31Algebraic CryptanalysisStep 1.Write a system of Multivariate Quadratic equations [MQ]Step 2.Solve it.Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 32ANF-to-CNF method - The Outsider[Courtois, Bard, Jefferson]Before we did try, we actually never believed it could work…☺ ☺ ☺Convert MQ to a SAT problem.(both are NP-hard problems)Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 33*ANF-to-CNF – Main IdeaPrinciple 1: each monomial = one dummy variable.d+1 clauses for each degree d monomialAlgebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 34*AlsoPrinciple 2: Handling XORs – Not obvious. Long XORsknown to be hard problems for SAT solvers.• Split longer XORs in several shorter with more dummy variables.• About 4 h clauses for a XOR of size h.Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 35*ANF-to-CNFThis description is enough to produce a working version.Space for non-trivial optimisations. See: Gregory V. Bard, Nicolas T. Courtois and Chris Jefferson: “Efficient Methods for Conversion and Solution of Sparse Systems of Low-Degree Multivariate Polynomials over GF(2) via SAT-Solvers”. eprint.iacr.org/2007/024Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 36Solving SATWhat are SAT solvers?Heuristic algorithms for solving SAT problems.• Guess some variables.• Examine consequences.• If a contradiction found, I can add a new clause saying “In this set of constraints one is false”.Very advanced area of research.Introduction for “dummies”: Gregory Bard PhD thesis.Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 37MiniSat 2.0. Winner of SAT-Race 2006 competition.An open-source SAT solver package, by Niklas Eén, Niklas Sörensson, http://www.cs.chalmers.se/Cs/Research/FormalMethods/MiniSat/Compiles with gcc under both Unix and Windows.Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 38**ANF-to-CNF + MiniSat 2.0.Gives amazing results in algebraic cryptanalysis of just any (not too complex/not too many rounds) cipher.  Also for random sparse MQ.• Certain VERY large systems solved in seconds on PC (thousands of variables !).• Few take a couple hours/days…• Then infeasible, we hit the wall…Jump from 0 to ¥.Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 39**What Can Be Done with SAT Solvers ?• Clearly it is not the size of the system but the nature of it.• Sometimes more powerful than Grobner Bases, sometimes less.Paradoxes: • If you guess some variables, can become much slower ☺.• Great variability in results (hard to compute an average running time, better to look at 20 % faster timings).• Memory:– For many cases tiny: 9 Mbytes while Magma hangs at > 2Gbytes for the same system.– For some working cases: 1.5 Gbytes and substantial time. Then terminates with the solution as well.Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 40Hitag2 ProtocolsAlgebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 41From Original Philips Specs • Found on a Russian web side(!)• Hitag 2 have two modes.– Password mode [less secure]– Crypto mode.• We focus on the crypto mode. Sort of challenge-response protocol. – Mutual authentication.– But the reader is authenticated first.• Prevents tag-only attacks, or attacks at home: – sniffed data is needed.Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 42Mutual Authentication in the Crypto mode• The tag sends:• The car picks a random IV (32 bits) and sends: • If the stream authenticator ks1 is correct, tag sends where PWST is a password, ks1,ks2 are the first 32+32 bits of Hitag 2 keystream initialised with (K,IV)11111 + (Config||PWST)Å ks25 + 32 bitsIV + ks132 + 32 bits11111 + SN5 +32 bitsAlgebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 43Sniffed Traces? We did not do the actual hacking of car keys.Some recorded Hitag2 traces can be found in [Nohl, Plotz HAR’09]https://har2009.org/program/attachments/113_breaking_hitag2_part1_hardware.pdfAlgebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 44Our ResultsAlgebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 45Our Chosen IV Attack [not practical]NOT practical.  • An active attacker can send the data to the tag, but the tag will NOT respond if the authenticator is incorrect…• Purely theoretical attack:– We need to know the ks1 for 16 authentication attempts with 16 chosen IVs in the counter mode (consecutive integers on 32 bits).– We combine 16 systems of equations. We don’t guess any bits.– The complete 48-bit key is then found in 6 hours on a PC with MiniSat 2.0. • The full attack is 6 hours total.Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 46Our Known IV Attack [practical !]This attack slower BUT it is practical given the protocol: • Sniffed data from 4 transactions needed.• 32 bits of the keystream per known IV are available (assuming PWST is already known). • We fix/guess 14 bits of the key and combine 4 systems of equations for 4 known IVs.– The solution is then found in 10 seconds on a PC with MiniSat 2.0. • The full attack on a full 48-bit key takes about 214*10 s which is less than 2 days. Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 47Cryptanalysis and the IndustryAlgebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 48Industry Impact?“old” industry:• Good excuse to replace these old systems. – Nobody thought they would be very secure by today’s standards…“new” industry:• Silicon hacking labs: we need to realize that: ⇒what people in Europe/US do so that they can evaluate the security of the product (and publish a nice paper)…, ⇒it will be done routinely in China and by several firmsBUT not for research, but for the manufacturing industry(and it will be legal: in Chinese law), Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 49*Example, cf. made-in-china.com:Supports: Mercedes, BMWAlgebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 50*Programmer 2: [All come from China]Supports: BMW (2002 -2009)CAS/CAS2/CAS3  CAS/CAS2/CAS3  CAS/CAS2/CAS3 DG512 / CAS3 +  DG512 / CAS3 +  DG512 / CAS3 + DP512 key and  DP512 key and  DP512 key and remote control remote control remote controlAlgebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 51*Programmer 3: [China]Audi A8, VW Touareg, VW Phaeton, Bentley Continental, Porsche Cayenne, BMWE38, E39, E46, E53, E60, E61,  E38, E39, E46, E53, E60, E61,  E38, E39, E46, E53, E60, E61, E63, E64, E65, E66, E87, E90,  E63, E64, E65, E66, E87, E90,  E63, E64, E65, E66, E87, E90, E91, E92 E91, E92 E91, E92Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 52*Programmer 4:  [China]Audi A8, VW Touareg, VW Phaeton, Bentley Continental, Porsche Cayenne, BMWE38, E39, E46, E53,  E38, E39, E46, E53,  E38, E39, E46, E53, E60, E61, E63, E64,  E60, E61, E63, E64,  E60, E61, E63, E64, E65, E66, E87, E90,  E65, E66, E87, E90,  E65, E66, E87, E90, E91, E92 E91, E92 E91, E92Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 53*Programmer 5:  [China]Audi A8, VW Touareg, VW Phaeton, Bentley Continental, Porsche Cayenne, BMWE38, E39, E46, E53,  E38, E39, E46, E53,  E38, E39, E46, E53, E60, E61, E63, E64,  E60, E61, E63, E64,  E60, E61, E63, E64, E65, E66, E87, E90,  E65, E66, E87, E90,  E65, E66, E87, E90, E91, E92 E91, E92 E91, E92Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 54ConclusionOld industrial ciphers can now be routinely broken by automated tools such as SAT solvers. The industry needs to recognise that:– Reverse engineering is cheaper and easier than ever. A microscope + software A microscope + software A microscope + software… … …– “Kindegarten crypto” fails.Algebraic Attacks on Hitag 2 CipherCourtois, O’Neil, Quisquater 55New Perspective for the Industry• Old / Kindegarten crypto fails.• Custom/secret crypto is OK.– But it needs to be evaluated and tested.We propose a new method to evaluate evaluate evaluate evaluate crypto algorithms used by the industry. • [OLD] private consulting…with selective disclosure.• [NEW] TODAY: Automated Cryptanalysis Automated Cryptanalysis Automated Cryptanalysis Automated CryptanalysisSpec of              Try ourthe cipher  =>     software no need to DISCLOSE the SPEC!

Practical Algebraic Attacks on the Hitag2 Stream Cipher in RFID Transponders

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