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Authenticated Encryption

  • Gen({--n) Tag(k,m) Vrfy(k.m,t)

  • In previous -lectures, we learned how to protect the Confidentiality of the Message. In L- integrity(& authenticity) is the new goal. Detecting rather than provention.

  • MA(MACs), (KG,E,D) vs. (Gen,Tag,Vrfy)→ key is not a secrecy.

  • existentially unforgeable

  • Why encryption not enough(Some Symmetric Encryptions such as SE based on PRG and SE based on ECB)

  • PRF → MAC(EU+CMA) ; How to extent?

    • Some bad examples. Tag(k,(m-m-)==>
      • (F(k,m-,F(k,m-) → Get the Tag(k,(m-m-) from Tag(k, (m-m-)
      • (F(k,m- ^ F(k,m-) → Get Tag(k,(m-m-) from Tag(k, (m-m-)
      • (F(k,-m-,F(k,-m-)→ Get Tag(k,(m-) from Tag(k,(m-m-)
      • (F(k,L|-m-,F(k,L|-m-) → Get Tag(k,(m-m-) from Tag(k,(m-m-) & Tag(k,(m-m-)
    • BC Modes(CBC, OFB, CTR) (length of output == input) → an improve → uses some mechanism like CBC to get a fixed-length output.

  • (Gen,H) collision-resistant hash functions, birthday attack, Merkle-Damgaard ((Gen,h)→(Gen,H)). MD-SHA-3

  • CRH → MACS

    • fixedTag(k-H(k-m))
    • H(k|m)
    • H(k' xor opad | H( k' xor ipad | m))

  • Application(Virus fingerprinting, Deduplication, File sharing, Merkle tree)

  • IND-CCA-secure Encryption

    • KG'=(KG(),Gen())→ k-k2
    • Enc'(k-k-m)=( Enc(k- m)→ c-t=Tag(k- c-) → c
    • Dec'(k- k- c) = Vrfy(k-c-t)+ Dec(k-c- -. Time stamp + session token (The final version)

  • A useful but not "useful" skill — hybrid proof.

  • some notation G() → RG(), R() or F()→ RF(),