342 research outputs found
Circular chosen-ciphertext security with compact ciphertexts
A key-dependent message (KDM) secure encryption scheme is secure even if an adversary obtains encryptions of messages that depend on the secret key. Such key-dependent encryptions naturally occur in scenarios such as harddisk encryption, formal cryptography, or in specific protocols. However, there are not many provably secure constructions of KDM-secure encryption schemes. Moreover, only one construction, due to Camenisch, Chandran, and Shoup (Eurocrypt 2009) is known to be secure against active (i.e., CCA) attacks.
In this work, we construct the first public-key encryption scheme that is KDM-secure against active adversaries and has compact ciphertexts. As usual, we allow only circular key dependencies, meaning that encryptions of arbitrary *entire* secret keys under arbitrary public keys are considered in a multi-user setting.
Technically, we follow the approach of Boneh, Halevi, Hamburg, and Ostrovsky (Crypto 2008) to KDM security, which however only achieves security against passive adversaries. We explain an inherent problem in adapting their techniques to active security, and resolve this problem using a new technical tool called ``lossy algebraic filters\u27\u27 (LAFs). We stress that we significantly deviate from the approach of Camenisch, Chandran, and Shoup to obtain KDM security against active adversaries. This allows us to develop a scheme with compact ciphertexts that consist only of a constant number of group elements
Classical Homomorphic Encryption for Quantum Circuits
We present the first leveled fully homomorphic encryption scheme for quantum
circuits with classical keys. The scheme allows a classical client to blindly
delegate a quantum computation to a quantum server: an honest server is able to
run the computation while a malicious server is unable to learn any information
about the computation. We show that it is possible to construct such a scheme
directly from a quantum secure classical homomorphic encryption scheme with
certain properties. Finally, we show that a classical homomorphic encryption
scheme with the required properties can be constructed from the learning with
errors problem
Naor-Yung paradigm with shared randomness and applications
The Naor-Yung paradigm (Naor and Yung, STOC’90) allows to generically boost security under chosen-plaintext attacks (CPA) to security against chosen-ciphertext attacks (CCA) for public-key encryption (PKE) schemes. The main idea is to encrypt the plaintext twice (under independent public keys), and to append a non-interactive zero-knowledge (NIZK) proof that the two ciphertexts indeed encrypt the same message. Later work by Camenisch, Chandran, and Shoup (Eurocrypt’09) and Naor and Segev (Crypto’09 and SIAM J. Comput.’12) established that the very same techniques can also be used in the settings of key-dependent message (KDM) and key-leakage attacks (respectively). In this paper we study the conditions under which the two ciphertexts in the Naor-Yung construction can share the same random coins. We find that this is possible, provided that the underlying PKE scheme meets an additional simple property. The motivation for re-using the same random coins is that this allows to design much more efficient NIZK proofs. We showcase such an improvement in the random oracle model, under standard complexity assumptions including Decisional Diffie-Hellman, Quadratic Residuosity, and Subset Sum. The length of the resulting ciphertexts is reduced by 50%, yielding truly efficient PKE schemes achieving CCA security under KDM and key-leakage attacks. As an additional contribution, we design the first PKE scheme whose CPA security under KDM attacks can be directly reduced to (low-density instances of) the Subset Sum assumption. The scheme supports keydependent messages computed via any affine function of the secret ke
Key Rotation for Authenticated Encryption
A common requirement in practice is to periodically rotate the keys used to
encrypt stored data. Systems used by Amazon and Google do so using a hybrid
encryption technique which is eminently practical but has questionable
security in the face of key compromises and does not provide full key
rotation. Meanwhile, symmetric updatable encryption schemes (introduced by
Boneh et al. CRYPTO 2013) support full key rotation without performing
decryption: ciphertexts created under one key can be rotated to ciphertexts
created under a different key with the help of a re-encryption token. By
design, the tokens do not leak information about keys or plaintexts and so
can be given to storage providers without compromising security. But the
prior work of Boneh et al. addresses relatively weak confidentiality goals
and does not consider integrity at all. Moreover, as we show, a subtle issue
with their concrete scheme obviates a security proof even for confidentiality
against passive attacks.
This paper presents a systematic study of updatable Authenticated Encryption
(AE). We provide a set of security notions that strengthen those in prior
work. These notions enable us to tease out real-world security requirements
of different strengths and build schemes that satisfy them efficiently. We
show that the hybrid approach currently used in industry achieves relatively
weak forms of confidentiality and integrity, but can be modified at low cost
to meet our stronger confidentiality and integrity goals. This leads to a
practical scheme that has negligible overhead beyond conventional AE. We then
introduce re-encryption indistinguishability, a security notion that formally
captures the idea of fully refreshing keys upon rotation. We show how to
repair the scheme of Boneh et al., attaining our stronger confidentiality
notion. We also show how to extend the scheme to provide integrity, and we
prove that it meets our re- encryption indistinguishability notion. Finally,
we discuss how to instantiate our scheme efficiently using off-the-shelf
cryptographic components (AE, hashing, elliptic curves). We report on the
performance of a prototype implementation, showing that fully secure key
rotations can be performed at a throughput of approximately 116 kB/s
Efficient Fully Homomorphic Encryption from (Standard) LWE
A fully homomorphic encryption (FHE) scheme allows anyone to transform an encryption of a message, m, into an encryption of any (efficient) function of that message, f(m), without knowing the secret key. We present a leveled FHE scheme that is based solely on the (standard) learning with errors (LWE) assumption. (Leveled FHE schemes are initialized with a bound on the maximal evaluation depth. However, this restriction can be removed by assuming “weak circular security.”) Applying known results on LWE, the security of our scheme is based on the worst-case hardness of “short vector problems” on arbitrary lattices. Our construction improves on previous
works in two aspects: 1. We show that “somewhat homomorphic” encryption can be based on LWE, using a new relinearization technique. In contrast, all previous schemes relied on complexity assumptions related to ideals in various rings. 2. We deviate from the “squashing paradigm” used
in all previous works. We introduce a new dimension-modulus reduction technique, which shortens the ciphertexts and reduces the decryption complexity of our scheme, without introducing additional
assumptions. Our scheme has very short ciphertexts, and we therefore use it to construct an asymptotically efficient LWE-based single-server private information retrieval (PIR) protocol. The communication complexity of our protocol (in the public-key model) is k·polylog(k)+log |DB| bits per
single-bit query, in order to achieve security against 2k-time adversaries (based on the best known attacks against our underlying assumptions). Key words. cryptology, public-key encryption, fully homomorphic encryption, learning with errors, private information retrieva
Sanitization of FHE ciphertexts
By definition, fully homomorphic encryption (FHE) schemes support homomorphic decryption, and all known FHE constructions are bootstrapped from a Somewhat Homomorphic Encryption (SHE) scheme via this technique. Additionally, when a public key is provided, ciphertexts are also re-randomizable, e.g., by adding to them fresh encryptions of 0. From those two operations we devise an algorithm to sanitize a ciphertext, by making its distribution canonical. In particular, the distribution of the ciphertext does not depend on the circuit that led to it via homomorphic evaluation, thus providing circuit privacy in the honest-but-curious model. Unlike the previous approach based on noise flooding, our approach does not degrade much the security/efficiency trade-off of the underlying FHE. The technique can be applied to all lattice-based FHE proposed so far, without substantially affecting their concrete parameters
Enabling Secure Database as a Service using Fully Homomorphic Encryption: Challenges and Opportunities
The database community, at least for the last decade, has been grappling with
querying encrypted data, which would enable secure database as a service
solutions. A recent breakthrough in the cryptographic community (in 2009)
related to fully homomorphic encryption (FHE) showed that arbitrary computation
on encrypted data is possible. Successful adoption of FHE for query processing
is, however, still a distant dream, and numerous challenges have to be
addressed. One challenge is how to perform algebraic query processing of
encrypted data, where we produce encrypted intermediate results and operations
on encrypted data can be composed. In this paper, we describe our solution for
algebraic query processing of encrypted data, and also outline several other
challenges that need to be addressed, while also describing the lessons that
can be learnt from a decade of work by the database community in querying
encrypted data
On the IND-CCA1 Security of FHE Schemes
Fully homomorphic encryption (FHE) is a powerful tool in cryptography that allows one to perform arbitrary computations on encrypted material without having to decrypt it first. There are numerous FHE schemes, all of which are expanded from somewhat homomorphic encryption (SHE) schemes, and some of which are considered viable in practice. However, while these FHE schemes are semantically (IND-CPA) secure, the question of their IND-CCA1 security is much less studied, and we therefore provide an overview of the IND-CCA1 security of all acknowledged FHE schemes in this paper. To give this overview, we grouped the SHE schemes into broad categories based on their similarities and underlying hardness problems. For each category, we show that the SHE schemes are susceptible to either known adaptive key recovery attacks, a natural extension of known attacks, or our proposed attacks. Finally, we discuss the known techniques to achieve IND-CCA1-secure FHE and SHE schemes. We concluded that none of the proposed schemes were IND-CCA1-secure and that the known general constructions all had their shortcomings.publishedVersio
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