## CryptoDB

### Shweta Agrawal

#### Affiliation: IIT Madras, India

#### Publications

**Year**

**Venue**

**Title**

2019

CRYPTO

Attribute Based Encryption (and more) for Nondeterministic Finite Automata from LWE
Abstract

Constructing Attribute Based Encryption (ABE) [56] for uniform models of computation from standard assumptions, is an important problem, about which very little is known. The only known ABE schemes in this setting that (i) avoid reliance on multilinear maps or indistinguishability obfuscation, (ii) support unbounded length inputs and (iii) permit unbounded key requests to the adversary in the security game, are by Waters from Crypto, 2012 [57] and its variants. Waters provided the first ABE for Deterministic Finite Automata (DFA) satisfying the above properties, from a parametrized or “q-type” assumption over bilinear maps. Generalizing this construction to Nondeterministic Finite Automata (NFA) was left as an explicit open problem in the same work, and has seen no progress to date. Constructions from other assumptions such as more standard pairing based assumptions, or lattice based assumptions has also proved elusive.In this work, we construct the first symmetric key attribute based encryption scheme for nondeterministic finite automata (NFA) from the learning with errors (LWE) assumption. Our scheme supports unbounded length inputs as well as unbounded length machines. In more detail, secret keys in our construction are associated with an NFA M of unbounded length, ciphertexts are associated with a tuple $$(\mathbf {x}, m)$$ where $$\mathbf {x}$$ is a public attribute of unbounded length and m is a secret message bit, and decryption recovers m if and only if $$M(\mathbf {x})=1$$.Further, we leverage our ABE to achieve (restricted notions of) attribute hiding analogous to the circuit setting, obtaining the first predicate encryption and bounded key functional encryption schemes for NFA from LWE. We achieve machine hiding in the single/bounded key setting to obtain the first reusable garbled NFA from standard assumptions. In terms of lower bounds, we show that secret key functional encryption even for DFAs, with security against unbounded key requests implies indistinguishability obfuscation ($$\mathsf {iO}$$) for circuits; this suggests a barrier in achieving full fledged functional encryption for NFA.

2019

EUROCRYPT

Indistinguishability Obfuscation Without Multilinear Maps: New Methods for Bootstrapping and Instantiation
Abstract

Constructing indistinguishability obfuscation ($$\mathsf{iO}$$iO) [17] is a central open question in cryptography. We provide new methods to make progress towards this goal. Our contributions may be summarized as follows:1.Bootstrapping. In a recent work, Lin and Tessaro [71] (LT) show that $$\mathsf{iO}$$iO may be constructed using (i) Functional Encryption ($$\mathsf {FE}$$FE) for polynomials of degree L, (ii) Pseudorandom Generators ($$\mathsf{PRG}$$PRG) with blockwise localityL and polynomial expansion, and (iii) Learning With Errors ($$\mathsf{LWE}$$LWE). Since there exist constructions of $$\mathsf {FE}$$FE for quadratic polynomials from standard assumptions on bilinear maps [16, 68], the ideal scenario would be to set $$L=2$$L=2, yielding $$\mathsf{iO}$$iO from widely believed assumptionsUnfortunately, it was shown soon after [18, 73] that $$\mathsf{PRG}$$PRG with block locality 2 and the expansion factor required by the LT construction, concretely $$\varOmega (n \cdot 2^{b(3+\epsilon )})$$Ω(n·2b(3+ϵ)), where n is the input length and b is the block length, do not exist. In the worst case, these lower bounds rule out 2-block local $$\mathsf{PRG}$$PRG with stretch $$\varOmega (n \cdot 2^{b(2+\epsilon )})$$Ω(n·2b(2+ϵ)). While [18, 73] provided strong negative evidence for constructing $$\mathsf{iO}$$iO based on bilinear maps, they could not rule out the possibility completely; a tantalizing gap has remained. Given the current state of lower bounds, the existence of 2 block local $$\mathsf{PRG}$$PRG with expansion factor $$\varOmega (n \cdot 2^{b(1+\epsilon )})$$Ω(n·2b(1+ϵ)) remains open, although this stretch does not suffice for the LT bootstrapping, and is hence unclear to be relevant for $$\mathsf{iO}$$iO.In this work, we improve the state of affairs as follows.(a)Weakening requirements on Boolean PRGs: In this work, we show that the narrow window of expansion factors left open by lower bounds do suffice for $$\mathsf{iO}$$iO. We show a new method to construct $$\mathsf {FE}$$FE for $$\mathsf {NC}_1$$NC1 from (i) $$\mathsf {FE}$$FE for degree L polynomials, (ii) $$\mathsf{PRG}$$PRGs of block locality L and expansion factor $$\tilde{\varOmega }(n \cdot 2^{b(1+\epsilon )})$$Ω~(n·2b(1+ϵ)), and (iii) $$\mathsf{LWE}$$LWE (or $$\mathsf{RLWE}$$RLWE).(b)Broadening class of sufficient randomness generators: Our bootstrapping theorem may be instantiated with a broader class of pseudorandom generators than hitherto considered for $$\mathsf{iO}$$iO, and may circumvent lower bounds known for the arithmetic degree of $$\mathsf{iO}$$iO-sufficient $$\mathsf{PRG}$$PRGs [18, 73]; in particular, these may admit instantiations with arithmetic degree 2, yielding $$\mathsf{iO}$$iO with the additional assumptions of $$\mathsf{SXDH}$$SXDH on Bilinear maps and $$\mathsf{LWE}$$LWE. In more detail, we may use the following two classes of $$\mathsf{PRG}$$PRG:i.Non-Boolean PRGs: We may use pseudorandom generators whose inputs and outputs need not be Boolean but may be integers restricted to a small (polynomial) range. Additionally, the outputs are not required to be pseudorandom but must only satisfy a milder indistinguishability property (We note that our notion of non Boolean PRGs is qualitatively similar to the notion of $$\varDelta $$Δ RGs defined in the concurrent work of Ananth, Jain and Sahai [9]. We emphasize that the methods of [9] and the present work are very different, but both works independently discover the same notion of weak PRG as sufficient for building $$\mathsf{iO}$$iO.).ii.Correlated Noise Generators: We introduce an even weaker class of pseudorandom generators, which we call correlated noise generators ($$\mathsf{CNG}$$CNG) which may not only be non-Boolean but are required to satisfy an even milder (seeming) indistinguishability property than $$\varDelta $$Δ RG.(c)Assumptions and Efficiency. Our bootstrapping theorems can be based on the hardness of the Learning With Errors problem or its ring variant ($$\mathsf{LWE}/ \mathsf{RLWE}$$LWE/RLWE) and can compile $$\mathsf {FE}$$FE for degree L polynomials directly to $$\mathsf {FE}$$FE for $$\mathsf {NC}_1$$NC1. Previous work compiles $$\mathsf {FE}$$FE for degree L polynomials to $$\mathsf {FE}$$FE for $$\mathsf {NC}_0$$NC0 to $$\mathsf {FE}$$FE for $$\mathsf {NC}_1$$NC1 to $$\mathsf{iO}$$iO [12, 45, 68, 72].Our method for bootstrapping to $$\mathsf {NC}_1$$NC1 does not go via randomized encodings as in previous works, which makes it simpler and more efficient than in previous works.2.Instantiating Primitives. In this work, we provide the first direct candidate of $$\mathsf {FE}$$FE for constant degree polynomials from new assumptions on lattices. Our construction is new and does not go via multilinear maps or graded encoding schemes as all previous constructions. Together with the bootstrapping step above, this yields a completely new candidate for$$\mathsf{iO}$$iO (as well as $$\mathsf {FE}$$FE for $$\mathsf {NC}_1$$NC1), which makes no use of multilinear or even bilinear maps. Our construction is based on the ring learning with errors assumption ($$\mathsf{RLWE}$$RLWE) as well as new untested assumptions on NTRU rings.We provide a detailed security analysis and discuss why previously known attacks in the context of multilinear maps, especially zeroizing and annihilation attacks, do not appear to apply to our setting. We caution that our construction must yet be subject to rigorous cryptanalysis by the community before confidence can be gained in its security. However, we believe that the significant departure from known multilinear map based constructions opens up a new and potentially fruitful direction to explore in the quest for $$\mathsf{iO}$$iO.Our construction is based entirely on lattices, due to which one may hope for post quantum security. Note that this feature is not enjoyed by instantiations that make any use of bilinear maps even if secure instances of weak PRGs, as identified by the present work, the follow-up by Lin and Matt [69] and the independent work by Ananth, Jain and Sahai [9] are found.

2018

TCC

FE and iO for Turing Machines from Minimal Assumptions
Abstract

We construct Indistinguishability Obfuscation ($$\mathsf {iO}$$) and Functional Encryption ($$\mathsf {FE}$$) schemes in the Turing machine model from the minimal assumption of compact $$\mathsf {FE}$$ for circuits ($$\mathsf {CktFE}$$). Our constructions overcome the barrier of sub-exponential loss incurred by all prior work. Our contributions are:1.We construct $$\mathsf {iO}$$ in the Turing machine model from the same assumptions as required in the circuit model, namely, sub-exponentially secure $$\mathsf {FE}$$ for circuits. The previous best constructions [6, 41] require sub-exponentially secure $$\mathsf {iO}$$ for circuits, which in turn requires sub-exponentially secure $$\mathsf {FE}$$ for circuits [5, 15].2.We provide a new construction of single input $$\mathsf {FE}$$ for Turing machines with unbounded length inputs and optimal parameters from polynomially secure, compact $$\mathsf {FE}$$ for circuits. The previously best known construction by Ananth and Sahai [7] relies on $$\mathsf {iO}$$ for circuits, or equivalently, sub-exponentially secure $$\mathsf {FE}$$ for circuits.3.We provide a new construction of multi-input $$\mathsf {FE}$$ for Turing machines. Our construction supports a fixed number of encryptors (say k), who may each encrypt a string $$\mathbf {x}_i$$ of unbounded length. We rely on sub-exponentially secure $$\mathsf {FE}$$ for circuits, while the only previous construction [10] relies on a strong knowledge type assumption, namely, public coin differing inputs obfuscation.
Our techniques are new and from first principles, and avoid usage of sophisticated $$\mathsf {iO}$$ specific machinery such as positional accumulators and splittable signatures that were used by all relevant prior work [6, 7, 41].

2012

CRYPTO

2010

EPRINT

Preventing Pollution Attacks in Multi-Source Network Coding
Abstract

Network coding is a method for achieving channel capacity in networks.
The key idea is to allow network routers to linearly mix packets as
they traverse the network so that recipients receive linear
combinations of packets. Network coded systems are vulnerable to
pollution attacks where a single malicious node floods the network
with bad packets and prevents the receiver from decoding correctly.
Cryptographic defenses to these problems are based on homomorphic
signatures and MACs. These proposals, however, cannot handle mixing of
packets from multiple sources, which is needed to achieve the full
benefits of network coding. In this paper we address integrity of
multi-source mixing. We propose a security model for this setting
and provide a generic construction.

#### Program Committees

- Asiacrypt 2019
- Crypto 2018
- PKC 2018
- TCC 2018
- Crypto 2017
- Asiacrypt 2017
- Eurocrypt 2016
- PKC 2015

#### Coauthors

- Shashank Agrawal (3)
- Saikrishna Badrinarayanan (1)
- Dan Boneh (4)
- Xavier Boyen (5)
- Yevgeniy Dodis (1)
- David Freeman (3)
- Craig Gentry (1)
- Sergey Gorbunov (1)
- Vipul Goyal (1)
- Shai Halevi (1)
- Abhishek Jain (1)
- Abishek Kumarasubramanian (1)
- Benoît Libert (1)
- Monosij Maitra (2)
- Manoj Prabhakaran (4)
- Alon Rosen (1)
- Amit Sahai (3)
- Damien Stehlé (1)
- Vinod Vaikuntanathan (4)
- Panagiotis Voulgaris (1)
- Hoeteck Wee (2)
- Daniel Wichs (1)
- Shota Yamada (1)