Partitioning via Non-linear Polynomial Functions: More Compact IBEs from Ideal Lattices and Bilinear Maps
04 Dec 2016-pp 682-712
TL;DR: In this paper, Chen et al. proposed a secure IBE scheme based on the hardness of a computational/search problem, rather than a decisional problem such as DDH and DLIN on bilinear maps with sublinear public parameter size.
Abstract: In this paper, we present new adaptively secure identity-based encryption IBE schemes. One of the distinguishing properties of the schemes is that it achieves shorter public parameters than previous schemes. Both of our schemes follow the general framework presented in the recent IBE scheme of Yamada Eurocrypt 2016, employed with novel techniques tailored to meet the underlying algebraic structure to overcome the difficulties arising in our specific setting. Specifically, we obtain the following:
- Our first scheme is proven secure under the ring learning with errors RLWE assumption and achieves the best asymptotic space efficiency among existing schemes from the same assumption. The main technical contribution is in our new security proof that exploits the ring structure in a crucial way. Our technique allows us to greatly weaken the underlying hardness assumption e.g., we assume the hardness of RLWE with a fixed polynomial approximation factor whereas Yamada's scheme requires a super-polynomial approximation factor while improving the overall efficiency.
- Our second IBE scheme is constructed on bilinear maps and is secure under the 3-computational bilinear Diffie-Hellman exponent assumption. This is the first IBE scheme based on the hardness of a computational/search problem, rather than a decisional problem such as DDH and DLIN on bilinear maps with sub-linear public parameter size.
Citations
More filters
Posted Content•
TL;DR: This work presents the first lattice-based IBE scheme with practical parameters and obtains digital signature schemes which are shorter than the previously most-compact ones of Ducas, Durmus, Lepoint, and Lyubashevsky from Crypto 2013.
Abstract: Efficient implementations of lattice-based cryptographic schemes have been limited to only the most basic primitives like encryption and digital signatures. The main reason for this limitation is that at the core of many advanced lattice primitives is a trapdoor sampling algorithm (Gentry, Peikert, Vaikuntanathan, STOC 2008) that produced outputs that were too long for practical applications. In this work, we show that using a particular distribution over NTRU lattices can make GPV-based schemes suitable for practice. More concretely, we present the first lattice-based IBE scheme with practical parameters – key and ciphertext sizes are between two and four kilobytes, and all encryption and decryption operations take approximately one millisecond on a moderately-powered laptop. As a by-product, we also obtain digital signature schemes which are shorter than the previously most-compact ones of Ducas, Durmus, Lepoint, and Lyubashevsky from Crypto 2013.
153 citations
15 Oct 2018
TL;DR: A group signature scheme, based on the hardness of lattice problems, whose outputs are more than an order of magnitude smaller than the currently most efficient schemes in the literature is presented.
Abstract: We present a group signature scheme, based on the hardness of lattice problems, whose outputs are more than an order of magnitude smaller than the currently most efficient schemes in the literature. Since lattice-based schemes are also usually non-trivial to efficiently implement, we additionally provide the first experimental implementation of lattice-based group signatures demonstrating that our construction is indeed practical -- all operations take less than half a second on a standard laptop. A key component of our construction is a new zero-knowledge proof system for proving that a committed value belongs to a particular set of small size. The sets for which our proofs are applicable are exactly those that contain elements that remain stable under Galois automorphisms of the underlying cyclotomic number field of our lattice-based protocol. We believe that these proofs will find applications in other settings as well. The motivation of the new zero-knowledge proof in our construction is to allow the efficient use of the selectively-secure signature scheme (i.e. a signature scheme in which the adversary declares the forgery message before seeing the public key) of Agrawal et al. (Eurocrypt 2010) in constructions of lattice-based group signatures and other privacy protocols. For selectively-secure schemes to be meaningfully converted to standard signature schemes, it is crucial that the size of the message space is not too large. Using our zero-knowledge proofs, we can strategically pick small sets for which we can provide efficient zero-knowledge proofs of membership.
62 citations
03 Jul 2017
TL;DR: In this article, Chen et al. proposed a new lattice-based RIBE scheme secure against exposure of a-priori bounded number of decryption keys (for every identity).
Abstract: A revocable identity-based encryption (RIBE) scheme, proposed by Boldyreva et al., provides a revocation functionality for managing a number of users dynamically and efficiently. To capture a realistic scenario, Seo and Emura introduced an additional important security notion, called decryption key exposure resistance (DKER), where an adversary is allowed to query short-term decryption keys. Although several RIBE schemes that satisfy DKER have been proposed, all the lattice-based RIBE schemes, e.g., Chen et al.’s scheme, do not achieve DKER, since they basically do not have the key re-randomization property, which is considered to be an essential requirement for achieving DKER. In particular, in every existing lattice-based RIBE scheme, an adversary can easily recover plaintexts if the adversary is allowed to issue even a single short-term decryption key query. In this paper, we propose a new lattice-based RIBE scheme secure against exposure of a-priori bounded number of decryption keys (for every identity). We believe that this bounded notion is still meaningful and useful from a practical perspective. Technically, to achieve the bounded security without the key re-randomization property, key updates in our scheme are short vectors whose corresponding syndrome vector changes in each time period. For this approach to work correctly and for the scheme to be secure, cover free families play a crucial role in our construction.
46 citations
07 Dec 2020
TL;DR: New functional encryption schemes that combine the access control functionality of attribute-based encryption with the possibility of performing linear operations on the encrypted data are constructed, providing further evidence that more expressive forms of functional encryption can be realized under standard assumptions and with little computational overhead.
Abstract: We construct new functional encryption schemes that combine the access control functionality of attribute-based 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.
38 citations
30 Oct 2017
TL;DR: The much weaker security model is exploited to provide a new construction for bounded collusion and random key IPFE from the learning with errors assumption (LWE), which enjoys improved efficiency compared to the scheme of Agrawal et al.
Abstract: We provide efficient constructions for trace-and-revoke systems with public traceability in the black-box confirmation model. Our constructions achieve adaptive security, are based on standard assumptions and achieve significant efficiency gains compared to previous constructions. Our constructions rely on a generic transformation from inner product functional encryption (IPFE) schemes to trace-and-revoke systems. Our transformation requires the underlying IPFE scheme to only satisfy a very weak notion of security -- the attacker may only request a bounded number of random keys -- in contrast to the standard notion of security where she may request an unbounded number of arbitrarily chosen keys. We exploit the much weaker security model to provide a new construction for bounded collusion and random key IPFE from the learning with errors assumption (LWE), which enjoys improved efficiency compared to the scheme of Agrawal et al. [CRYPTO'16]. Together with IPFE schemes from Agrawal et al., we obtain trace and revoke from LWE, Decision Diffie Hellman and Decision Composite Residuosity.
37 citations
References
More filters
19 Aug 2001
TL;DR: This work proposes a fully functional identity-based encryption scheme (IBE) based on the Weil pairing that has chosen ciphertext security in the random oracle model assuming an elliptic curve variant of the computational Diffie-Hellman problem.
Abstract: We propose a fully functional identity-based encryption scheme (IBE). The scheme has chosen ciphertext security in the random oracle model assuming an elliptic curve variant of the computational Diffie-Hellman problem. Our system is based on the Weil pairing. We give precise definitions for secure identity based encryption schemes and give several applications for such systems.
7,083 citations
23 Aug 1985
TL;DR: In this article, the authors introduce a novel type of cryptographic scheme, which enables any pair of users to communicate securely and to verify each other's signatures without exchanging private or public keys, without keeping key directories, and without using the services of a third party.
Abstract: In this paper we introduce a novel type of cryptographic scheme, which enables any pair of users to communicate securely and to verify each other’s signatures without exchanging private or public keys, without keeping key directories, and without using the services of a third party. The scheme assumes the existence of trusted key generation centers, whose sole purpose is to give each user a personalized smart card when he first joins the network. The information embedded in this card enables the user to sign and encrypt the messages he sends and to decrypt and verify the messages he receives in a totally independent way, regardless of the identity of the other party. Previously issued cards do not have to be updated when new users join the network, and the various centers do not have to coordinate their activities or even to keep a user list. The centers can be closed after all the cards are issued, and the network can continue to function in a completely decentralized way for an indefinite period.
6,902 citations
22 May 2005
TL;DR: A public-key cryptosystem whose hardness is based on the worst-case quantum hardness of SVP and SIVP, and an efficient solution to the learning problem implies a quantum, which can be made classical.
Abstract: Our main result is a reduction from worst-case lattice problems such as SVP and SIVP to a certain learning problem. This learning problem is a natural extension of the 'learning from parity with error' problem to higher moduli. It can also be viewed as the problem of decoding from a random linear code. This, we believe, gives a strong indication that these problems are hard. Our reduction, however, is quantum. Hence, an efficient solution to the learning problem implies a quantum algorithm for SVP and SIVP. A main open question is whether this reduction can be made classical.Using the main result, we obtain a public-key cryptosystem whose hardness is based on the worst-case quantum hardness of SVP and SIVP. Previous lattice-based public-key cryptosystems such as the one by Ajtai and Dwork were only based on unique-SVP, a special case of SVP. The new cryptosystem is much more efficient than previous cryptosystems: the public key is of size O(n2) and encrypting a message increases its size by O(n)(in previous cryptosystems these values are O(n4) and O(n2), respectively). In fact, under the assumption that all parties share a random bit string of length O(n2), the size of the public key can be reduced to O(n).
2,620 citations
22 May 2005
TL;DR: This work first presents their IBE construction and reduces the security of the scheme to the decisional Bilinear Diffie-Hellman (BDH) problem, and shows that their techniques can be used to build a new signature scheme that is secure under the computational Diffie -Hellman assumption without random oracles.
Abstract: We present the first efficient Identity-Based Encryption (IBE) scheme that is fully secure without random oracles We first present our IBE construction and reduce the security of our scheme to the decisional Bilinear Diffie-Hellman (BDH) problem Additionally, we show that our techniques can be used to build a new signature scheme that is secure under the computational Diffie-Hellman assumption without random oracles
2,188 citations
02 May 2004
TL;DR: The first secure IBE scheme without random oracles was presented in this article, where the adversary must commit ahead of time to the identity that it intends to attack, whereas in the standard model the adversary is allowed to choose this identity adaptively.
Abstract: We construct two efficient Identity Based Encryption (IBE) systems that are selective identity secure without the random oracle model. Selective identity secure IBE is a slightly weaker security model than the standard security model for IBE. In this model the adversary must commit ahead of time to the identity that it intends to attack, whereas in the standard model the adversary is allowed to choose this identity adaptively. Our first secure IBE system extends to give a selective identity Hierarchical IBE secure without random oracles.
1,917 citations