Indistinguishability Obfuscation Without Multilinear Maps: New Paradigms via Low Degree Weak Pseudorandomness and Security Amplification

Ananth, Prabhanjan; Jain, Aayush; Lin, Hongfei; Matt, Christian; Sahai, Amit

doi:10.1007/978-3-030-26954-8_10

Cited by 46 publications

(12 citation statements)

References 77 publications

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“…In prior works [AJS18,JLMS19], the authors define a so-called partially-hiding FE allowing for the computation on two inputs (x, y), where the input x is seen as a public attribute and the other one, y, remains hidden. The construction of [AJKS18] supports degree-2 computation on the private input y, and degree-1 computation on the public input x. Its security rely on the generic bilinear group model.…”

Section: Multi-input Extensionsmentioning

confidence: 99%

“…Its security rely on the generic bilinear group model. In [JLMS19], functional secret keys support the computation of degree-2 polynomials on the private input, as in [AJKS18], but it supports NC 0 computation on the public input. As an additional benefit, the security of their construction rely on a standard assumption on pairing groups (namely, SXDH).…”

Section: Multi-input Extensionsmentioning

confidence: 99%

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Inner-Product Functional Encryption with Fine-Grained Access Control

Abdalla

Catalano

Ursu

2020

Lecture Notes in Computer Science

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We construct new functional encryption schemes that combine the access control functionality of attributebased encryption with the possibility of performing linear operations on the encrypted data. While such a primitive could be easily realized from fully fledged functional encryption schemes, what makes our result interesting is the fact that our schemes simultaneously achieve all the following properties. They are public-key, efficient and can be proved secure under standard and well established assumptions (such as LWE or pairings). Furthermore, security is guaranteed in the setting where adversaries are allowed to get functional keys that decrypt the challenge ciphertext. Our first results are two functional encryption schemes for the family of functions that allow users to embed policies (expressed by monotone span programs) in the encrypted data, so that one can generate functional keys to compute weighted sums on the latter. Both schemes are pairing-based and quite generic: they combine the ALS functional encryption scheme for inner products from Crypto 2016 with any attribute-based encryption schemes relying on the dual-system encryption methodology. As an additional bonus, they yield simple and elegant multi-input extensions essentially for free, thereby broadening the set of applications for such schemes. Multi-input is a particularly desirable feature in our setting, since it gives a finer access control over the encrypted data, by allowing users to associate different access policies to different parts of the encrypted data. Our second result builds identity-based functional encryption for inner products from lattices. This is achieved by carefully combining existing IBE schemes from lattices with adapted, LWE-based, variants of ALS. We point out to intrinsic technical bottlenecks to obtain richer forms of access control from lattices. From a conceptual point of view, all our results can be seen as further evidence that more expressive forms of functional encryption can be realized under standard assumptions and with little computational overhead.

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Section: Multi-input Extensionsmentioning

confidence: 99%

Section: Multi-input Extensionsmentioning

confidence: 99%

Inner-Product Functional Encryption with Fine-Grained Access Control

Abdalla

Catalano

Ursu

2020

Lecture Notes in Computer Science

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“…• A recent series of works demonstrated a close connection between building functional encryption (and thus IO) to that of low-degree pseudorandom generators (PRG) over the integers [35,5,2], where the role of the PRGs is to flood any leakage from the error term during FHE decryption [30]. Here, we show to exploit matrix PRFs -again over the integersto flood any leakage from the error term in the GGH15 encodings (but unlike the setting of PRGs, we do not require the output of the PRFs to have polynomially bounded domain).…”

Section: Discussionmentioning

confidence: 99%

“…where + is computed over Z. A similar relaxation has been considered in the context of weaker pseudorandom generators for building IO [5]. For this notion, one could potentially have candidates where each M i,b is drawn uniformly at random from a Gaussian distribution but where v M R is the same as in Section 6.1.2.…”

Section: Securitymentioning

confidence: 99%

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Matrix PRFs: Constructions, Attacks, and Applications to Obfuscation

Chen

Hhan

Vaikuntanathan

et al. 2019

Lecture Notes in Computer Science

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We initiate a systematic study of pseudorandom functions (PRFs) that are computable by simple matrix branching programs; we refer to these objects as "matrix PRFs". Matrix PRFs are attractive due to their simplicity, strong connections to complexity theory and group theory, and recent applications in program obfuscation.Our main results are:• We present constructions of matrix PRFs based on the conjectured hardness of computational problems pertaining to matrix products.

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Optimal Broadcast Encryption from Pairings and LWE

Agrawal

Yamada

2020

Lecture Notes in Computer Science

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Indistinguishability Obfuscation Without Multilinear Maps: New Paradigms via Low Degree Weak Pseudorandomness and Security Amplification

Cited by 46 publications

References 77 publications

Inner-Product Functional Encryption with Fine-Grained Access Control

Inner-Product Functional Encryption with Fine-Grained Access Control

Matrix PRFs: Constructions, Attacks, and Applications to Obfuscation

Optimal Broadcast Encryption from Pairings and LWE

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