Modeling Memory Faults in Signature and Authenticated Encryption Schemes
- 2 Citations
- 840 Downloads
Abstract
Memory fault attacks, inducing errors in computations, have been an ever-evolving threat to cryptographic schemes since their discovery for cryptography by Boneh et al. (Eurocrypt 1997). Initially requiring physical tampering with hardware, the software-based rowhammer attack put forward by Kim et al. (ISCA 2014) enabled fault attacks also through malicious software running on the same host machine. This led to concerning novel attack vectors, for example on deterministic signature schemes, whose approach to avoid dependency on (good) randomness renders them vulnerable to fault attacks. This has been demonstrated in realistic adversarial settings in a series of recent works. However, a unified formalism of different memory fault attacks, enabling also to argue the security of countermeasures, is missing yet.
In this work, we suggest a generic extension for existing security models that enables a game-based treatment of cryptographic fault resilience. Our modeling specifies exemplary memory fault attack types of different strength, ranging from random bit-flip faults to differential (rowhammer-style) faults to full adversarial control on indicated memory variables. We apply our model first to deterministic signatures to revisit known fault attacks as well as to establish provable guarantees of fault resilience for proposed fault-attack countermeasures. In a second application to nonce-misuse resistant authenticated encryption, we provide the first fault-attack treatment of the SIV mode of operation and give a provably secure fault-resilient variant.
Keywords
Fault attacks Security model Fault resilience Deterministic signatures Nonce-misuse resistant authenticated encryptionNotes
Acknowledgments
Felix Günther is supported in part by Research Fellowship grant GU 1859/1-1 of the German Research Foundation (DFG) and National Science Foundation (NSF) grants CNS-1526801 and CNS-1717640. This work has been co-funded by the DFG as part of project P2 within the CRC 1119 CROSSING. Most of the work on this paper was done while Felix Günther was at UC San Diego.
References
- 1.Ambrose, C., Bos, J.W., Fay, B., Joye, M., Lochter, M., Murray, B.: Differential attacks on deterministic signatures. In: Smart, N.P. (ed.) CT-RSA 2018. LNCS, vol. 10808, pp. 339–353. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-76953-0_18CrossRefGoogle Scholar
- 2.Aranha, D.F., Orlandi, C., Takahashi, A., Zaverucha, G.: Security of hedged Fiat-Shamir signatures under fault attacks. Cryptology ePrint Archive, Report 2019/956 (2019). https://eprint.iacr.org/2019/956
- 3.Bar-El, H., Choukri, H., Naccache, D., Tunstall, M., Whelan, C.: The sorcerer’s apprentice guide to fault attacks. Proc. IEEE 94(2), 370–382 (2006)CrossRefGoogle Scholar
- 4.Barenghi, A., Breveglieri, L., Koren, I., Naccache, D.: Fault injection attacks on cryptographic devices: theory, practice, and countermeasures. Proc. IEEE 100(11), 3056–3076 (2012)CrossRefGoogle Scholar
- 5.Barenghi, A., Pelosi, G.: A note on fault attacks against deterministic signature schemes. In: Ogawa, K., Yoshioka, K. (eds.) IWSEC 2016. LNCS, vol. 9836, pp. 182–192. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-44524-3_11CrossRefGoogle Scholar
- 6.Barthe, G., Dupressoir, F., Fouque, P.-A., Grégoire, B., Tibouchi, M., Zapalowicz, J.-C.: Making RSA–PSS provably secure against non-random faults. In: Batina, L., Robshaw, M. (eds.) CHES 2014. LNCS, vol. 8731, pp. 206–222. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44709-3_12CrossRefGoogle Scholar
- 7.Bellare, M., et al.: Hedged public-key encryption: how to protect against bad randomness. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 232–249. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-10366-7_14CrossRefGoogle Scholar
- 8.Bellare, M., Cash, D.: Pseudorandom functions and permutations provably secure against related-key attacks. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 666–684. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14623-7_36CrossRefGoogle Scholar
- 9.Bellare, M., Cash, D., Miller, R.: Cryptography secure against related-key attacks and tampering. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 486–503. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-25385-0_26CrossRefGoogle Scholar
- 10.Bellare, M., Goldreich, O., Goldwasser, S.: Incremental cryptography: the case of hashing and signing. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 216–233. Springer, Heidelberg (1994). https://doi.org/10.1007/3-540-48658-5_22CrossRefGoogle Scholar
- 11.Bellare, M., Goldreich, O., Goldwasser, S.: Incremental cryptography and application to virus protection. In: 27th ACM STOC, pp. 45–56. ACM Press, May/Jun 1995Google Scholar
- 12.Bellare, M., Kohno, T.: Hash function balance and its impact on birthday attacks. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 401–418. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24676-3_24CrossRefGoogle Scholar
- 13.Bellare, M., Paterson, K.G., Rogaway, P.: Security of symmetric encryption against mass surveillance. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part I. LNCS, vol. 8616, pp. 1–19. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44371-2_1CrossRefGoogle Scholar
- 14.Bellare, M., Rogaway, P.: Random oracles are practical: a paradigm for designing efficient protocols. In: Denning, D.E., Pyle, R., Ganesan, R., Sandhu, R.S., Ashby, V. (eds.) ACM CCS 93, pp. 62–73. ACM Press, November 1993Google Scholar
- 15.Bellare, M., Rogaway, P.: The exact security of digital signatures-how to sign with RSA and Rabin. In: Maurer, U. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 399–416. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-68339-9_34CrossRefGoogle Scholar
- 16.Bernstein, D.J., Duif, N., Lange, T., Schwabe, P., Yang, B.-Y.: High-speed high-security signatures. In: Preneel, B., Takagi, T. (eds.) CHES 2011. LNCS, vol. 6917, pp. 124–142. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-23951-9_9CrossRefGoogle Scholar
- 17.Biehl, I., Meyer, B., Müller, V.: Differential fault attacks on elliptic curve cryptosystems. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 131–146. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-44598-6_8CrossRefGoogle Scholar
- 18.Biham, E., Shamir, A.: Differential fault analysis of secret key cryptosystems. In: Kaliski, B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 513–525. Springer, Heidelberg (1997). https://doi.org/10.1007/BFb0052259CrossRefGoogle Scholar
- 19.Blömer, J., Günther, P.: Singular curve point decompression attack. In: 2015 Workshop on Fault Diagnosis and Tolerance in Cryptography (FDTC), pp. 71–84 (2015)Google Scholar
- 20.Boneh, D., DeMillo, R.A., Lipton, R.J.: On the importance of checking cryptographic protocols for faults (extended abstract). In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 37–51. Springer, Heidelberg (1997). https://doi.org/10.1007/3-540-69053-0_4CrossRefGoogle Scholar
- 21.Breitner, J., Heninger, N.: Biased nonce sense: lattice attacks against weak ECDSA signatures in cryptocurrencies. In: Goldberg, I., Moore, T. (eds.) FC 2019. LNCS, vol. 11598, pp. 3–20. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-32101-7_1CrossRefGoogle Scholar
- 22.Brengel, M., Rossow, C.: Identifying key leakage of bitcoin users. In: Bailey, M., Holz, T., Stamatogiannakis, M., Ioannidis, S. (eds.) RAID 2018. LNCS, vol. 11050, pp. 623–643. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00470-5_29CrossRefGoogle Scholar
- 23.CAESAR: Competition for authenticated encryption: Security, applicability, and robustness. https://competitions.cr.yp.to/caesar.html
- 24.CERT Vulnerability Notes Database: Vulnerability note VU#925211: Debian and Ubuntu OpenSSL packages contain a predictable random number generator (2008). https://www.kb.cert.org/vuls/id/925211
- 25.Coron, J.-S., Mandal, A.: PSS is secure against random fault attacks. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 653–666. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-10366-7_38CrossRefGoogle Scholar
- 26.Dobraunig, C., Eichlseder, M., Korak, T., Lomné, V., Mendel, F.: Statistical fault attacks on nonce-based authenticated encryption schemes. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016, Part I. LNCS, vol. 10031, pp. 369–395. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53887-6_14CrossRefGoogle Scholar
- 27.Dobraunig, C., Mangard, S., Mendel, F., Primas, R.: Fault attacks on nonce-based authenticated encryption: application to keyak and ketje. In: Cid, C., Jacobson, M.J. (eds.) SAC 2018. LNCS, vol. 11349, pp. 257–277. Springer, Heidelberg (2019). https://doi.org/10.1007/978-3-030-10970-7_12CrossRefGoogle Scholar
- 28.Dorrendorf, L., Gutterman, Z., Pinkas, B.: Cryptanalysis of the windows random number generator. In: Ning, P., De Capitani di Vimercati, S., Syverson, P.F. (eds.) ACM CCS 2007, pp. 476–485. ACM Press, October 2007Google Scholar
- 29.Dworkin, M.: Recommendation for block cipher modes of operation: Galois/Counter Mode (GCM) and GMAC, November 2007. nIST Special Publication 800–38DGoogle Scholar
- 30.fail0verflow: Console hacking 2010: PS3 epic fail. In: 27th Chaos Communication Congress. Chaos Computer Club (2010)Google Scholar
- 31.Fischlin, M., Günther, F.: Modeling memory faults in signature and authenticated encryption schemes. Cryptology ePrint Archive, Report 2019/1053 (2019). https://eprint.iacr.org/2019/1053
- 32.Fouque, P.-A., Guillermin, N., Leresteux, D., Tibouchi, M., Zapalowicz, J.-C.: Attacking RSA–CRT signatures with faults on montgomery multiplication. In: Prouff, E., Schaumont, P. (eds.) CHES 2012. LNCS, vol. 7428, pp. 447–462. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-33027-8_26CrossRefGoogle Scholar
- 33.Gennaro, R., Lysyanskaya, A., Malkin, T., Micali, S., Rabin, T.: Algorithmic tamper-proof (ATP) security: theoretical foundations for security against hardware tampering. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 258–277. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24638-1_15CrossRefGoogle Scholar
- 34.Goldberg, I., Wagner, D.: Randomness and the Netscape browser. Dr. Dobb’s J. 21, 66–71 (1996)Google Scholar
- 35.Gueron, S., Lindell, Y.: GCM-SIV: full nonce misuse-resistant authenticated encryption at under one cycle per byte. In: Ray, I., Li, N., Kruegel, C. (eds.) ACM CCS 2015, pp. 109–119. ACM Press, October 2015Google Scholar
- 36.Gutterman, Z., Pinkas, B., Reinman, T.: Analysis of the linux random number generator. In: 2006 IEEE Symposium on Security and Privacy, pp. 371–385. IEEE Computer Society Press, May 2006Google Scholar
- 37.Ishai, Y., Prabhakaran, M., Sahai, A., Wagner, D.: Private circuits II: keeping secrets in tamperable circuits. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 308–327. Springer, Heidelberg (2006). https://doi.org/10.1007/11761679_19CrossRefzbMATHGoogle Scholar
- 38.Joux, A.: Authentication failures in NIST version of GCM (2006). http://csrc.nist.gov/groups/ST/toolkit/BCM/documents/Joux_comments.pdf
- 39.Joye, M., Lenstra, A.K., Quisquater, J.J.: Chinese remaindering based cryptosystems in the presence of faults. J. Cryptol. 12(4), 241–245 (1999)CrossRefGoogle Scholar
- 40.Kim, Y., et al.: Flipping bits in memory without accessing them: an experimental study of DRAM disturbance errors. In: Proceeding of the 41st Annual International Symposium on Computer Architecuture, ISCA 2014, pp. 361–372. IEEE Press, Piscataway, NJ, USA (2014)Google Scholar
- 41.Lenstra, A.K.: Memo on RSA signature generation in the presence of faults (1996)Google Scholar
- 42.May, T.C., Woods, M.H.: A new physical mechanism for soft errors in dynamic memories. In: 16th International Reliability Physics Symposium, pp. 33–40, April 1978Google Scholar
- 43.McGrew, D.A., Viega, J.: The security and performance of the Galois/Counter Mode (GCM) of operation. In: Canteaut, A., Viswanathan, K. (eds.) INDOCRYPT 2004. LNCS, vol. 3348, pp. 343–355. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30556-9_27CrossRefGoogle Scholar
- 44.M’Raïhi, D., Naccache, D., Pointcheval, D., Vaudenay, S.: Computational alternatives to random number generators. In: Tavares, S., Meijer, H. (eds.) SAC 1998. LNCS, vol. 1556, pp. 72–80. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48892-8_6CrossRefGoogle Scholar
- 45.Namprempre, C., Rogaway, P., Shrimpton, T.: Reconsidering generic composition. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 257–274. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-55220-5_15CrossRefGoogle Scholar
- 46.National Institute of Standards and Technology: Digital Signature Standard (DSS) (FIPS PUB 186–4), July 2013Google Scholar
- 47.Perrin, T.: The XEdDSA and VXEdDSA signature schemes (2016). https://signal.org/docs/specifications/xeddsa/
- 48.Poddebniak, D., Somorovsky, J., Schinzel, S., Lochter, M., Rösler, P.: Attacking deterministic signature schemes using fault attacks. In: 2018 IEEE European Symposium on Security and Privacy, EuroS&P 2018, pp. 338–352. IEEE, April 2018Google Scholar
- 49.Pornin, T.: Deterministic Usage of the Digital Signature Algorithm (DSA) and Elliptic Curve Digital Signature Algorithm (ECDSA). RFC 6979 (Informational), August 2013. https://www.rfc-editor.org/rfc/rfc6979.txt
- 50.Razavi, K., Gras, B., Bosman, E., Preneel, B., Giuffrida, C., Bos, H.: Flip Feng Shui: hammering a needle in the software stack. In: Holz, T., Savage, S. (eds.) USENIX Security 2016, pp. 1–18. USENIX Association, August 2016Google Scholar
- 51.Rogaway, P.: Authenticated-encryption with associated-data. In: Atluri, V. (ed.) ACM CCS 2002, pp. 98–107. ACM Press, November 2002Google Scholar
- 52.Rogaway, P.: Nonce-based symmetric encryption. In: Roy, B., Meier, W. (eds.) FSE 2004. LNCS, vol. 3017, pp. 348–358. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-25937-4_22CrossRefzbMATHGoogle Scholar
- 53.Rogaway, P., Shrimpton, T.: A provable-security treatment of the key-wrap problem. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 373–390. Springer, Heidelberg (2006). https://doi.org/10.1007/11761679_23CrossRefGoogle Scholar
- 54.Romailler, Y., Pelissier, S.: Practical fault attack against the Ed25519 and EdDSA signature schemes. In: 2017 Workshop on Fault Diagnosis and Tolerance in Cryptography (FDTC), pp. 17–24 (2017)Google Scholar
- 55.Samwel, N., Batina, L.: Practical fault injection on deterministic signatures: the case of EdDSA. In: Joux, A., Nitaj, A., Rachidi, T. (eds.) AFRICACRYPT 2018. LNCS, vol. 10831, pp. 306–321. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-89339-6_17CrossRefGoogle Scholar
- 56.Samwel, N., Batina, L., Bertoni, G., Daemen, J., Susella, R.: Breaking Ed25519 in WolfSSL. In: Smart, N.P. (ed.) CT-RSA 2018. LNCS, vol. 10808, pp. 1–20. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-76953-0_1CrossRefzbMATHGoogle Scholar
- 57.Schmidt, B.: [curves] EdDSA specification (2016). https://moderncrypto.org/mail-archive/curves/2016/000768.html
- 58.Signal: Technical documentation. https://whispersystems.org/docs/
- 59.Takahashi, A., Tibouchi, M.: Degenerate fault attacks on elliptic curve parameters in OpenSSL. In: 2019 IEEE European Symposium on Security and Privacy, EuroS&P 2019. IEEE, June 2019, to appearGoogle Scholar
- 60.Vaudenay, S.: The security of DSA and ECDSA. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 309–323. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36288-6_23CrossRefGoogle Scholar
- 61.Ylonen, T., Lonvick, C. (ed.) The Secure Shell (SSH) Authentication Protocol. RFC 4252 (Proposed Standard), January 2006. https://www.rfc-editor.org/rfc/rfc4252.txt, updated by RFCs 8308, 8332