*22:17* [Pub][ePrint]
Constrained Key-Homomorphic PRFs from Standard Lattice Assumptions Or: How to Secretly Embed a Circuit in Your PRF, by Zvika Brakerski and Vinod Vaikuntanathan
Boneh et al. (Crypto 13) and Banerjee and Peikert (Crypto 14) constructed pseudorandom functions (PRFs) from the Learning with Errors (LWE) assumption by embedding combinatorial objects, a path and a tree respectively, in instances of the LWE problem. In this work, we show how to generalize this approach to embed circuits, inspired by recent progress in the study of Attribute Based Encryption.Embedding a universal circuit for some class of functions allows us to produce constrained keys for functions in this class, which gives us the first standard-lattice-assumption-based constrained PRF (CPRF) for general bounded-description bounded-depth functions, for arbitrary polynomial bounds on the description size and the depth. (A constrained key w.r.t a circuit $C$ enables one to evaluate the PRF on all $x$ for which $C(x)=1$, but reveals nothing on the PRF values at other points.) We rely on the LWE assumption and on the one-dimensional SIS (Short Integer Solution) assumption, which are both related to the worst case hardness of general lattice problems. Previous constructions for similar function classes relied on such exotic assumptions as the existence of multilinear maps or secure program obfuscation. The main drawback of our construction is that it does not allow collusion (i.e. to provide more than a single constrained key to an adversary).

Similarly to the aforementioned previous works, our PRF family is also key homomorphic.

Interestingly, our constrained keys are very short. Their length does not depend directly either on the size of the constraint circuit or on the input length.

We are not aware of any prior construction achieving this property, even relying on strong assumptions such as indistinguishability obfuscation.

*19:17* [Pub][ePrint]
Obfuscating Circuits via Composite-Order Graded Encoding, by Benny Applebaum and Zvika Brakerski
We present a candidate obfuscator based on composite-order Graded Encoding Schemes (GES), which are a generalization of multilinear maps. Our obfuscator operates on circuits directly without converting them into formulas or branching programs as was done in previous solutions. As a result, the time and size complexity of the obfuscated program, measured by the number of GES elements, is directly proportional to the circuit complexity of the program being obfuscated. This improves upon previous constructions whose complexity was related to the formula or branching program size. Known instantiations of Graded Encoding Schemes allow us to obfuscate circuit classes of polynomial degree, which include for example families of circuits of logarithmic depth.We prove that our obfuscator is secure against a class of generic algebraic attacks, formulated by a generic graded encoding model. We further consider a more robust model which provides more power to the adversary and extend our results to this setting as well.

As a secondary contribution, we define a new simple notion of \\emph{algebraic security} (which was implicit in previous works) and show that it captures standard security relative to an ideal GES oracle.

*19:17* [Pub][ePrint]
On the Regularity of Lossy RSA: Improved Bounds and Applications to Padding-Based Encryption, by Adam Smith and Ye Zhang
We provide new bounds on how close to regular the map x |--> x^e is on arithmetic progressions in Z_N, assuming e | Phi(N) and N is composite. We use these bounds to analyze the security of natural cryptographic problems related to RSA, based on the well-studied Phi-Hiding assumption. For example, under this assumption, we show that RSA PKCS #1 v1.5 is secure against chosen-plaintext attacks for messages of length roughly (log N)/4 bits, whereas the previous analysis, due to Lewko et al (2013), applies only to messages of length less than (log N)/32.In addition to providing new bounds, we also show that a key lemma of Lewko et al. is incorrect. We prove a weaker version of the claim which is nonetheless sufficient for most, though not all, of their applications.

Our technical results can be viewed as showing that exponentiation in Z_N is a deterministic extractor for every source that is uniform on an arithmetic progression. Previous work showed this type of statement only on average over a large class of sources, or for much longer progressions (that is, sources with much more entropy).

*19:17* [Pub][ePrint]
Predicate Encryption for Circuits from LWE, by Sergey Gorbunov and Vinod Vaikuntanathan and Hoeteck Wee
In predicate encryption, a ciphertext is associated with descriptiveattribute values $x$ in addition to a plaintext $\\mu$, and a secret key is associated with a predicate $f$. Decryption returns plaintext

$\\mu$ if and only if $f(x) = 1$. Moreover, security of predicate

encryption guarantees that an adversary learns nothing about the attribute $x$ or the plaintext $\\mu$ from a ciphertext, given arbitrary many secret keys that are not authorized to decrypt the ciphertext individually.

We construct a leveled predicate encryption scheme for all circuits, assuming the hardness of the subexponential learning with errors (LWE) problem. That is, for any polynomial function $d = d(\\secp)$,

we construct a predicate encryption scheme for the class of all circuits with depth bounded by $d(\\secp)$, where $\\secp$ is the security parameter.

*19:17* [Pub][ePrint]
Tight Parallel Repetition Theorems for Public-Coin Arguments using KL-divergence, by Kai-Min Chung and Rafael Pass
We present a new and conceptually simpler proof of a tight parallel-repetition theorem for public-coin arguments (Pass-Venkitasubramaniam, STOC\'07, Hastad et al, TCC\'10, Chung-Liu, TCC\'10). We follow the same proof framework as the previous non-tight parallel-repetition theorem of Hastad et al---which relied on *statistical distance* to measure the distance between experiments---and show that it can be made tight (and further simplied) if instead relying on *KL-divergence* as the distance between the experiments.We then show that our proof technique directly yields tight ``Chernoff-type\'\' parallel-repetition theorems (where one considers a ``threshold\'\' verifier that accepts iff the prover manages to convince a certain fraction of the parallel verifiers, as opposed to all of them) for any public-coin interactive argument; previously, tight results were only known for either constant-round protocols, or when the gap between the threshold and the original error-probability is a constant.

*19:17* [Pub][ePrint]
Constrained Key-Homomorphic PRFs from Standard Lattice Assumptions Or: How to Secretly Embed a Circuit in Your PRF, by Zvika Brakerski and Vinod Vaikuntanthan
Boneh et al. (Crypto 13) and Banerjee and Peikert (Crypto 14) constructed pseudorandom functions (PRFs) from the Learning with Errors (LWE) assumption by embedding combinatorial objects, a path and a tree respectively, in instances of the LWE problem. In this work, we show how to generalize this approach to embed circuits, inspired by recent progress in the study of Attribute Based Encryption.Embedding a universal circuit for some class of functions allows us to produce constrained keys for functions in this class, which gives us the first standard-lattice-assumption-based constrained PRF (CPRF) for general bounded-description bounded-depth functions, for arbitrary polynomial bounds on the description size and the depth. (A constrained key w.r.t a circuit $C$ enables one to evaluate the PRF on all $x$ for which $C(x)=1$, but reveals nothing on the PRF values at other points.) We rely on the LWE assumption and on the one-dimensional SIS (Short Integer Solution) assumption, which are both related to the worst case hardness of general lattice problems. Previous constructions for similar function classes relied on such exotic assumptions as the existence of multilinear maps or secure program obfuscation. The main drawback of our construction is that it does not allow collusion (i.e. to provide more than a single constrained key to an adversary).

Similarly to the aforementioned previous works, our PRF family is also key homomorphic.

Interestingly, our constrained keys are very short. Their length does not depend directly either on the size of the constraint circuit or on the input length.

We are not aware of any prior construction achieving this property, even relying on strong assumptions such as indistinguishability obfuscation.

*03:30* [Job][New]
Post-Doc, Ph.D. student, *University of Massachusetts Amherst*
For two NSF projects in the area of hardware Trojans we are looking for post-docs and Ph.D. students who are interested in research that bridge applied cryptography and modern hardware design. Both projects are very exciting and cutting-edge. We are looking for candidates which have previous experience in one of the two areas:Topic Area 1) Applied cryptography, hardware security, implementation attacks

Topic Area 2) VLSI design, FPGA design, circuit design, embedded systems

Candidates for the post-doc position should have a strong publication record in the leading cryptography conferences (Topic Area 1) or leading computer engineering journals (Topic Area 2). Candidates for the Ph.D. position should have a BS&MS degree with excellent grades, relevant course work and some initial experience in one of the topic areas, either through MS-level research or industry.

The candidates should be open to work in an interdisciplinary fashion, i.e., to conduct high-quality research that bridges applied cryptography and modern hardware design. They will collaborate with Christof Paar (applied cryptography, on leave from the Univ. of Bochum) as well as Sandip Kundu and Russ Tessier (both computer engineering) at UMass Amherst. It is expected that the candidates also interact with researchers at the University of Bochum.

Sounds interesting? Please send your resume (CV, transcript of records) and names/email addresses of two people how can provide references.