By Matthew Robshaw, Jonathan Katz

The 3 volume-set, LNCS 9814, LNCS 9815, and LNCS 9816, constitutes the refereed complaints of the thirty sixth Annual overseas Cryptology convention, CRYPTO 2016, held in Santa Barbara, CA, united states, in August 2016.

The 70 revised complete papers awarded have been conscientiously reviewed and chosen from 274 submissions. The papers are equipped within the following topical sections: provable protection for symmetric cryptography; uneven cryptography and cryptanalysis; cryptography in thought and perform; compromised platforms; symmetric cryptanalysis; algorithmic quantity idea; symmetric primitives; uneven cryptography; symmetric cryptography; cryptanalytic instruments; hardware-oriented cryptography; safe computation and protocols; obfuscation; quantum innovations; spooky encryption; IBE, ABE, and useful encryption; computerized instruments and synthesis; 0 wisdom; theory.

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Extra info for Advances in Cryptology – CRYPTO 2016: 36th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 14-18, 2016, Proceedings, Part II (Lecture Notes in Computer Science)

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Key Generation: Gen(1λ ) generates (P P, SP ) ← ParamsGen(1λ ) and σ ← $ SampleInj(P P ). It also chooses a hash function H ← H. It outputs a public key P K = (P P, σ, H) and a secret key SK = (SP, H). Encryption: Enc takes as input a public key P K = (P P, σ, H) and a message $ msg ∈ {0, 1} . It chooses x ← {0, 1}n , sets C1 := Evaluation(P P, σ, x) and C2 := msg ⊕ H(x) and outputs C = (C1 , C2 ) Decryption: Dec takes as input a secret key SK = (SP, H) and a ciphertext C = (C1 , C2 ), computes x := Inversion(SP, σ, C1 ) and msg := C2 ⊕ H(x), and outputs msg.

In order to circumvent the above problem we make a simple probabilistic argument. In our reduction, about one half of the multi-user public-keys are coming from the MU-UF-KOA experiment, for the other half the reduction knows the corresponding secret-keys. Which secret-keys are known is hidden from the adversary’s view. Now, if the multi-user adversary first obtains a signature on message m under pk1 and then submits a forgery on the same message m under pk2 , the reduction hopes for the good case that one of the public-keys comes from the MU-UF-KOA experiment and the other one is known.

C∗ ∈ (k) Let view be the view from A in Game 8 except K ∗ , and view := {P K, C ∗ , {xi,j mod ord(S)}i∈[λ],j∈[n],k∈{0,1} }. By a similar argument as in the proof of Claim 3, we have Δ((K ∗ , view), (U, view)) ≤ Δ((K ∗ , H, view ), (U, H, view )) and (t ) (t ) ˜ ∞ (C ∗ λi=1 xi,1i , . . , C ∗ λi=1 xi,ni |view ) ≥ n log p¯ ≥ n( B − 1) ≥ (2 N + 1)λ. H $ λ (ti ) λ (ti ) If we let X := (C ∗ i=1 xi,1 , . . , C ∗ i=1 xi,n ), Y := view and δ := 2− N λ in Lemma 2, then we have Δ((K ∗ , H, view ), (U, H, view )) ≤ 2− N λ where K ∗ = ∗ ∗ $ H(C ∗ x1 +t y1 , .

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