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Subdividing Crypto with Smart Cards

2. Smart Card Cryptography. Smart cards are ideal for cryptographic operationsBut not all cryptographic operations can (or should) be implemented on smart cardsQuestion: How to subdivide securely between smart cards and other components?. 3. Security Assumptions. Typical assumptions about opponen

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Subdividing Crypto with Smart Cards

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    1. Subdividing Crypto with Smart Cards Burt Kaliski, RSA Laboratories May 2, 2000 CardTech/SecurTech 2000

    2. 2 Smart Card Cryptography Smart cards are ideal for cryptographic operations But not all cryptographic operations can (or should) be implemented on smart cards Question: How to subdivide securely between smart cards and other components?

    3. 3 Security Assumptions Typical assumptions about opponent: 1. Knows specification of operation 2. Has full knowledge of output 3. May have full knowledge of input “known input” attack 4. May have full control of input “chosen input” attack 5. Has no access to internals Design goal: prove operation secure under these assumptions

    4. 4 Achieving the Goal Typical security proofs focus on full operation, not individual elements i.e., “no access to internals” With a smart card implementation, proof must focus on how operations are subdivided Most methods can have acceptable security if subdivided, but some need special modifications

    5. 5 Attack Model Generally, a user may control access to smart card operations with a PIN Access to operations is thus limited to opponents who know the PIN But what if a hostile reader? What if a hostile user? e.g., private key on smart card owned by someone else Opponent’s goal: one or more undetected results extreme case: total compromise of private key

    6. 6 Example Scenarios Signature generation Key unwrapping … both operations with private key

    7. 7 Signature Generation User signs message with private key: ? = SignK(M) Typical model: hash, pad, signature primitive 1. h = Hash(M) 2. x = Pad(h) 3. ? = SigPrimK(x) Security generally based on full SignK operation

    8. 8 Example: PKCS #1 v1.5 Signature method based on RSA algorithm, in widespread use Hash = MD5 or SHA-1 Pad(h) = 00 01 ff ff … ff ff 00 . HashID . h SigPrim(x) = xd mod n

    9. 9 Signature Generation

    10. 10 Signature Generation

    11. 11 Signature Generation

    12. 12 Signature Generation

    13. 13 Assessment Full operation may be impractical, because message may be too long Signature primitive only may be insecure, because “raw” access given to private key at least a loss of assurance potential loss of “tracing,” e.g., via blind signatures Primitive + pad is “just about right” short input no raw access but a security proof would be even better and smart card must know about padding method

    14. 14 Hash vs. Message Hostile reader can change the hash But if card does the hashing, reader can still change the message ? Hash, message essentially the same w.r.t. message integrity If card needs to “know” what it’s signing, should sign a smaller message containing critical fields, hash of rest

    15. 15 Key Unwrapping User recovers symmetric key with private key: k = UnwrapK(c) (presumably, another user has wrapped k) Typical model: decryption primitive, unpad 1. x = DecPrimK(c) 2. k = Unpad(x) Security generally based on full UnwrapK operation

    16. 16 Assessment Decryption primitive only may be insecure, because “raw” access given to private key Primitive + unpad is “just about right” (with appropriate padding method) short input no raw access security proof is often available, e.g., OAEP encryption (OAEP = Optimal Asymmetric Encryption Padding [Bellare and Rogaway, 1994], as in PKCS #1 v2.0)

    17. 17 Symmetric Key vs. Message Hostile reader can read the symmetric key But if card does the decryption, reader can read the message ? Key, message essentially the same w.r.t. message confidentiality, if one message per key If more than one message per key, then card should keep the key

    18. 18 Case Study: PSS New signature method with provable security (Bellare and Rogaway, 1996) based on RSA algorithm proposed for PKCS #1 v2.1, IEEE P1363a, ISO/IEC 9796-2 Initial model: randomized hash, pad, signature primitive 1. h = Hash(M, salt), where salt random 2. x = Pad(h, salt) 3. ? = SigPrimK(x) Security based on full SignK operation

    19. 19 Details of Initial PSS Hash = SHA-1, etc. Pad(h, salt) = 00 . h . (G(h) xor (salt . 00 … 00)) where G is mask generation function SigPrim(x) = xd mod n Provable security under random oracle model Hash, G viewed as “black box” assumes opponent can only control message, not hash value “heuristic” security if opponent can control hash

    20. 20 Assessment Full operation may be impractical, because message may be too long Signature primitive only may be insecure, because “raw” access given to private key Primitive + pad is not “just about right” security proof assumes that attacker cannot control hash value

    21. 21 Revised PSS Alternative model to accommodate subdivision: hash, (randomized) pad, signature primitive 1. h = Hash(M) 2. x = Pad(h) 3. ? = SigPrimK(x) Security for full SignK operation, and for primitive + pad Additional benefit: protection against fault analysis attacks

    22. 22 Details of Revised PSS Hash = SHA-1, etc. Pad(h) = 00 . w . (G(w) xor (salt . 00 … 01)) where w = Hash(h, salt) salted hash has been moved inside some details omitted, e.g., header and trailer fields SigPrim(x) = xd mod n Provable security, even if attacker can control hash value

    23. 23 Conclusions Smart cards are ideal for cryptographic operations But cryptographic methods haven’t always been designed for smart cards New methods, like PSS, should take subdivision of operations into account

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