By Magnús M. Halldórsson, Kazuo Iwama, Naoki Kobayashi, Bettina Speckmann

The two-volume set LNCS 9134 and LNCS 9135 constitutes the refereed complaints of the forty second overseas Colloquium on Automata, Languages and Programming, ICALP 2015, held in Kyoto, Japan, in July 2015. The 143 revised complete papers awarded have been rigorously reviewed and chosen from 507 submissions. The papers are prepared within the following 3 tracks: algorithms, complexity, and video games; good judgment, semantics, automata, and concept of programming; and foundations of networked computation: versions, algorithms, and data management.

**Read Online or Download Automata, Languages, and Programming: 42nd International Colloquium, ICALP 2015, Kyoto, Japan, July 6-10, 2015, Proceedings, Part I PDF**

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**Additional info for Automata, Languages, and Programming: 42nd International Colloquium, ICALP 2015, Kyoto, Japan, July 6-10, 2015, Proceedings, Part I**

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Proof. We construct an SRE for DLWE here. On input an instance of size n, the encoder, decoder, simulator compute parameters m, , δ, p as functions of n. Encoding. The algorithm encSRE (1n , A, b) is deﬁned as follows. $ $ $ 1. Pick R ← [−p2/3 , p2/3 ]m×m , r0 ← [−p2/3+3δ , p2/3+3δ ]m , t ← Znp . 2. Set A = RA and b = r0 + Rb. 3. Output (A , b ) = (A , A t + b ). Decoding. The algorithm decSRE (1n , A , b ) accepts if and only if there exist 2/3+4δ 2/3+4δ ,p ]. x ∈ Znp , e ∈ Zm p , such that b = A x + e , and e ∈ [−p Simulation.

4 Oracle Separation Between SRE and SZK In this section, we crucially use the following Lemma about the class ( , δ)-SRE. This Lemma follows directly from the deﬁnition of ( , δ)-SRE. Lemma 1. Let Ex denote the distribution enc(x, r) for the algorithm enc(·, ·) of a language L admitting an ( , δ)-SRE, induced for any input x by picking r uni∗ formly at random in {0, 1} . Then, Δ(Ex , Ex ) ≤ 2 iﬀ f (x) = f (x ) (equivalently, both x, x ∈ L or both x, x ∈ L). Moreover, Δ(Ex , Ex ) ≥ 1 − 2δ iﬀ f (x) = f (x ) (equivalently, either x ∈ L, x ∈ L or x ∈ L, x ∈ L).

We construct an SRE for DLWE here. On input an instance of size n, the encoder, decoder, simulator compute parameters m, , δ, p as functions of n. Encoding. The algorithm encSRE (1n , A, b) is deﬁned as follows. $ $ $ 1. Pick R ← [−p2/3 , p2/3 ]m×m , r0 ← [−p2/3+3δ , p2/3+3δ ]m , t ← Znp . 2. Set A = RA and b = r0 + Rb. 3. Output (A , b ) = (A , A t + b ). Decoding. The algorithm decSRE (1n , A , b ) accepts if and only if there exist 2/3+4δ 2/3+4δ ,p ]. x ∈ Znp , e ∈ Zm p , such that b = A x + e , and e ∈ [−p Simulation.