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Self Protecting Cryptosystems

This article discusses the risks of key exposure in cryptographic systems and explores various approaches for protecting keys, including tamper-resistant hardware, secret sharing, and key-evolving cryptosystems.

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Self Protecting Cryptosystems

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  1. Self Protecting Cryptosystems Moti Yung Columbia University/ RSA Labs

  2. Key Exposure • The security of most cryptosystems relies crucially on some secret information (keys) • What if these keys are lost, stolen, or otherwise exposed? • In some application environments, key exposure represents a very serious risk

  3. Example: RSA public: N=pq, secret: primes p, q - RSA: <N,e> public key - message=M encryption: Me mod N. - decryption: M d mod N where d º e-1 mod f (N)

  4. Some Examples… • The threat of key exposure is increased as cryptographic algorithms are deployed on inexpensive, lightweight, and mobile devices • PDAs, mobile phones, laptops, … • Ad-hoc/sensor networks; “disposable” devices • Key exposure may also occur as a result of poor key management

  5. The Threat • Key exposure can be a devastating attack! • When secret keys are revealed, all security guarantees are typically gone • Once there are no more secrets, the situation seems hopeless… • In signature schemes, the owner may claim the key is stolen for “repudiation”…… • Can anything be done?

  6. Possible Approaches • Avoidance: Tamper-resistant hardware (with no side channel Attacks) • Decreasing likelihood of exposure (spread risk): • Secret sharing • Threshold cryptography • Server-aided cryptography • Proactive systems • Time-stamping server • Containment of key exposure (self-protection): • Key-evolving cryptosystems

  7. Different Protections for different Architectures • Distributed Systems: Many units perform the “sign” or “decrypt” – agents acting in a system is changed to a distributed entity • Key Evolving: A single Unit act as Cryptographic Container (e.g., one cellphone)

  8. Key-Evolving Cryptosystems • Time is divided into N periods (e.g., days) • Secret key stored on a device is dynamically updated over time • Public key (when applicable) remains fixed • Exposure of the key at period i affects only a limited number of other time periods • End of period: update– for self protection

  9. Different Paradigms • Forward security • Key-insulated security • Intrusion-resilience • Applicable to essentially any cryptographic functionality (public-/private- key authentication, encryption, signatures, etc.)

  10. Forward Security (Anderson ‘97) • Fixed public key PK; initial secret key SK0 • At time period i, device locally computes SKi = Upd(SKi-1) • Public-key operation uses PK and i • Secret-key operation uses SKi

  11. Forward Security… • Note: Exposure of SKi necessarily implies that the system is “broken” for t  i • This is implied by the model… • What about periods t < i?

  12. Secure exposed insecure (non-exposed) Goal • If the Upd function is one-way, exposure of SKi does not necessarily reveal SKi-1 (!) • Exploiting this, forward-secure systems guarantee that exposure of SKi does not affect security of the system for anyt < i SK0 SK1 … SKi-1 SKi SKi+1 … SKN

  13. E.g., Forward-Secure Signatures • Signature on a message m is a pair (i, ) where i is the period at which m was signed • Verification uses fixed public key PK; in effect, verifying that m was signed at time i • Even if adversary learns SKi for any i (in addition to signatures on chosen messages), cannot forge signatures for time periods t < i

  14. Using Forward-Secure Signatures • If a user learns that key exposure occurred at period i, she simply announces this fact • Signatures for time periods subsequent to i are no longer accepted as valid • Non-repudiation? (it helps limit repudiation as time moves)

  15. Secure Constructions (Signatures) • Anderson ‘97 • Secret-key size O(N) • Bellare-Miner ‘99 (also, formal definitions) • Signing/verifying require O(N) time • Krawczyk ‘00, Abdalla-Reyzin ‘00, Itkis-Reyzin ‘01, Malkin-Micciancio-Miner ‘02 • Various tradeoffs; O(log(N)) complexity possible

  16. Other Forward-Secure Systems • Forward-secrecy in key exchange protocols (e.g., [Diffie-van Oorschot-Weiner ‘92]) • Forward-secure shared-key cryptography [Bellare-Yee ‘03] • Threshold forward-secure signatures [Abdalla-Miner-Namprempre ‘01, Tzeng-Tzeng ‘02] • More recently: forward-secure PKE [Canetti, Halevi Katz ’03]

  17. Drawbacks of Forward-Security • Once SKi is exposed, no protection for future time periods • Indeed, impossible in this model • Forward-secure schemes are less efficient than “standard” schemes • Can we gain anything by assuming some protected storage?

  18. Key-Insulated Security [DKXY02] • “Server” • Secure, protected storage; likely immobile • Perhaps computationally-limited • Not necessarily trusted • “Device” • Mobile; inherently vulnerable to key exposure • Performs all actual cryptographic operations

  19. Key-Insulated Security • Time is divided into N periods and the public key is fixed, as before • Device updates its key by interacting with the server at the beginning of each period • Device itself performs all crypto operations for the remainder of the period --- this is not a threshold scheme (though motivated by threshold proactive systems)

  20. SK1 SK2 SK3 SK* SKN … Server Device time

  21. Possible Instantiations • E.g.: • Server = docking station; device = mobile phone • Server = desktop computer; device = laptop • Server = base station; device = sensor node • Etc. In the mobile world– period based “delegation” and exchange make sense.

  22. secure exposed Security Guarantees • Can achieve stronger security guarantees than in forward-secure systems • If SKi1,SKi2,…,SKitare exposed, only these time periods are (necessarily) “broken” • All other periods t {i1,…,it} remain “secure”! SK0 SK1 … SKi-1 SKi SKi+1 … SKN

  23. Additional Security Guarantees • Possible to additionally protect against an untrusted server • Clearly, in this case the server cannot simply send SKi • Possible to protect against eavesdropping on server/device communication • Clearly, in this case the server cannot simply send SK*

  24. More Formally… • (t, N)-security: Following exposure of up to t (arbitrary) secret keys, all unexposed time periods remain secure • Strong (t, N)-security: Additionally guarantees security against an untrusted server • Secure key updates (informally): Eavesdropping on communication between the device and the server is equivalent to key exposure at adjacent periods

  25. Connection with ID-based • ID-based scheme  key-insulated scheme achieving (N-1, N)-security • View time periods as IDs • However: IBE may be “overkill” • Computationally expensive (e.g., compared to RSA or El Gamal) • (t, N)-security (with t << N) may be enough

  26. Some Additional Work • Construction of (t, N)-key-insulated PKE from generic PKE [DKXY02] • Further analysis of key-insulated PKE [BP02] • Recently– private key • Constructions of (N-1, N)-key-insulated signature schemes [DKXY03] • In turn gives new constructions of ID-based signature schemes

  27. Intrusion-Resilience [IR02] • Combines forward-security and key-insulation to give the strongest security model (so far…) • Key-insulation guarantees security only when device keys are compromised • In general, compromise of both the server and the device (at any time) “breaks” the system

  28. Intrusion-Resilience • Key concept: secret keys evolve on both the device and the server…

  29. SK1 SK’1 SK2 SK’2 SK3 SK’3 SKN SK’N … … Server Device time

  30. Security Guarantees • If the keys on the device and the server are exposed for disjoint time periods, scheme achieves key-insulated security • If the keys on the device and the server are exposed for the same time period, scheme achieves forward security

  31. To Illustrate… • If the device is compromised for periods i1, …, it and the server is compromised for all other time periods, time periods t  {i1,…,it} remain secure • Even if the server alone is compromised for all time periods, all time periods remain secure • If the device and the server are both compromised at time i, time periods t < i remain secure

  32. Intrusion-Resilient Schemes • Intrusion-resilient signature schemes [Itkis-Reyzin ‘02, Itkis ‘03] • Intrusion-resilient PKE [DFKMY03]

  33. Comparison… • Forward-security • Device is self-sufficient; no need for a “server” • Key-insulation • If a server is available, provides stronger security guarantees • Schemes designed for this model are currently the most efficient • The only one with random access applications

  34. Comparison… • Intrusion-resilience • Achieves the strongest level of security • But…since intrusion-resilient schemes also achieve forward-security, such schemes can be no more efficient than forward-secure ones • If the server is trusted/secure, this level of security may be “overkill”

  35. The rest • I will cover various schemes in the various models • Will mention briefly distributed schemes • Will cover the various key evolving paradigms

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