# Point-Function Obfuscation: A Framework and Generic Constructions

@article{Bellare2015PointFunctionOA, title={Point-Function Obfuscation: A Framework and Generic Constructions}, author={Mihir Bellare and Igors Stepanovs}, journal={IACR Cryptol. ePrint Arch.}, year={2015}, volume={2015}, pages={703} }

We give a definitional framework for point-function obfuscation in which security is parameterized by a class of algorithms we call target generators. Existing and new notions are captured and explained as corresponding to different choices of this class. This leads to an elegant question: Is it possible to provide a generic construction, meaning one that takes an arbitrary class of target generators and returns a point-function obfuscator secure for it? We answer this in the affirmative with…

## 33 Citations

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## References

SHOWING 1-10 OF 58 REFERENCES

### On obfuscating point functions

- Mathematics, Computer ScienceSTOC '05
- 2005

This work provides a simple construction of efficient obfuscators for point functions for a slightly relaxed notion of obfuscation, and yields the first non-trivial obfuscator under general assumptions in the standard model.

### Obfuscating Point Functions with Multibit Output

- Computer Science, MathematicsEUROCRYPT
- 2008

A notion of obfuscation that is preserved under an appropriate composition operation is defined, which can be used to construct obfuscators of point functions with multibit output and other related functions.

### On Strong Simulation and Composable Point Obfuscation

- Computer Science, MathematicsJournal of Cryptology
- 2013

This work studies a simple relaxation of VBB: allow the simulator unbounded computation time, while still allowing only polynomially many queries to the oracle, and shows composable VGB-obfuscators for point programs under a strong variant of the Decision Diffie–Hellman assumption.

### Obfuscation for Cryptographic Purposes

- Computer Science, MathematicsJournal of Cryptology
- 2009

The results show that, while it is hard to avoid generic impossibilities, useful and reasonable obfuscation definitions are possible when considering specific tasks (i.e., function families), and several natural classes of functions for which their definitions yield interesting results.

### Indistinguishability Obfuscation versus Multi-bit Point Obfuscation with Auxiliary Input

- Mathematics, Computer ScienceASIACRYPT
- 2014

In a recent celebrated breakthrough, Garg et al. (FOCS 2013) gave the first candidate for so-called indistinguishability obfuscation (iO) thereby reviving the interest in obfuscation for a general…

### How to use indistinguishability obfuscation: deniable encryption, and more

- Computer Science, MathematicsIACR Cryptol. ePrint Arch.
- 2013

The 16-year-old open question of Deniable Encryption is resolved by giving the first construction of deniable encryption that does not require any pre-planning by the party that must later issue a denial.

### Poly-Many Hardcore Bits for Any One-Way Function and a Framework for Differing-Inputs Obfuscation

- Mathematics, Computer ScienceASIACRYPT
- 2013

The construction for injective one-way functions extends to extract hardcore bits on multiple, correlated inputs, yielding new D-PKE schemes and a definitional framework for differing-inputs obfuscation in which security is parameterized by circuit-sampler classes.

### On Symmetric Encryption and Point Obfuscation

- Computer Science, MathematicsTCC
- 2010

We show tight connections between several cryptographic primitives, namely encryption with weakly random keys, encryption with key-dependent messages (KDM), and obfuscation of point functions with…

### Instantiating Random Oracles via UCEs

- Computer Science, MathematicsIACR Cryptol. ePrint Arch.
- 2013

This paper provides a (standard-model) notion of security for (keyed) hash functions, called UCE, that we show enables instantiation of random oracles (ROs) in a fairly broad and systematic way.…

### Indistinguishability Obfuscation from the Multilinear Subgroup Elimination Assumption

- Computer Science, Mathematics2015 IEEE 56th Annual Symposium on Foundations of Computer Science
- 2015

This work provides the first construction of general-purpose indistinguishability obfuscation proven secure via a reduction to a natural computational assumption over multilinear maps, namely, the MultilInear Subgroup Elimination Assumption.