We propose a fully homomorphic encryption scheme -- i.e., a scheme that allows one to evaluate circuits over encrypted data without being able to decrypt. Our solution comes in three steps. First, we provide a general result -- that, to construct an encryption scheme that permits evaluation of arbitrary circuits, it suffices to construct an encryption scheme that can evaluate (slightly augmented versions of) its own decryption circuit; we call a scheme that can evaluate its (augmented) decryption circuit bootstrappable.Next, we describe a public key encryption scheme using ideal lattices that is almost bootstrappable.Lattice-based cryptosystems typically have decryption algorithms with low circuit complexity, often dominated by an inner product computation that is in NC1. Also, ideal lattices provide both additive and multiplicative homomorphisms (modulo a public-key ideal in a polynomial ring that is represented as a lattice), as needed to evaluate general circuits.Unfortunately, our initial scheme is not quite bootstrappable -- i.e., the depth that the scheme can correctly evaluate can be logarithmic in the lattice dimension, just like the depth of the decryption circuit, but the latter is greater than the former. In the final step, we show how to modify the scheme to reduce the depth of the decryption circuit, and thereby obtain a bootstrappable encryption scheme, without reducing the depth that the scheme can evaluate. Abstractly, we accomplish this by enabling the encrypter to start the decryption process, leaving less work for the decrypter, much like the server leaves less work for the decrypter in a server-aided cryptosystem.

/pdf/fully-homomorphic-encryption-using-ideal-lattices-3oirjo0huq.pdf

Fully homomorphic encryption using ideal lattices

In 1998, Blaze, Bleumer, and Strauss (BBS) proposed an application called atomic proxy re-encryption, in which a semitrusted proxy converts a ciphertext for Alice into a ciphertext for Bob without seeing the underlying plaintext. We predict that fast and secure re-encryption will become increasingly popular as a method for managing encrypted file systems. Although efficiently computable, the wide-spread adoption of BBS re-encryption has been hindered by considerable security risks. Following recent work of Dodis and Ivan, we present new re-encryption schemes that realize a stronger notion of security and demonstrate the usefulness of proxy re-encryption as a method of adding access control to a secure file system. Performance measurements of our experimental file system demonstrate that proxy re-encryption can work effectively in practice.

/pdf/improved-proxy-re-encryption-schemes-with-applications-to-1ugoecwezg.pdf

Improved proxy re-encryption schemes with applications to secure distributed storage

We describe a short signature scheme which is existentially unforgeable under a chosen message attack without using random oracles. The security of our scheme depends on a new complexity assumption we call the Strong Diffie-Hellman assumption. This assumption has similar properties to the Strong RSA assumption, hence the name. Strong RSA was previously used to construct signature schemes without random oracles. However, signatures generated by our scheme are much shorter and simpler than signatures from schemes based on Strong RSA. Furthermore, our scheme provides a limited form of message recovery.

/pdf/short-signatures-without-random-oracles-20yc7dm4ve.pdf

Short Signatures Without Random Oracles

We present as-strong-as-possible definitions of privacy, and constructions achieving them, for public-key encryption schemes where the encryption algorithm is deterministic. We obtain as a consequence database encryption methods that permit fast (i.e. sub-linear, and in fact logarithmic, time) search while provably providing privacy that is as strong as possible subject to this fast search constraint. One of our constructs, called RSA-DOAEP, has the added feature of being length preserving, so that it is the first example of a public-key cipher. We generalize this to obtain a notion of efficiently-searchable encryption schemes which permit more flexible privacy to search-time trade-offs via a technique called bucketization. Our results answer much-asked questions in the database community and provide foundations for work done there.

/pdf/deterministic-and-efficiently-searchable-encryption-by0gb957lb.pdf

Deterministic and efficiently searchable encryption

An authenticated encryption scheme is a symmetric encryption scheme whose goal is to provide both privacy and integrity. We consider two possible notions of authenticity for such schemes, namely integrity of plaintexts and integrity of ciphertexts, and relate them, when coupled with IND-CPA (indistinguishability under chosen-plaintext attack), to the standard notions of privacy IND-CCA and NM-CPA (indistinguishability under chosen-ciphertext attack and nonmalleability under chosen-plaintext attack) by presenting implications and separations between all notions considered. We then analyze the security of authenticated encryption schemes designed by “generic composition,” meaning making black-box use of a given symmetric encryption scheme and a given MAC. Three composition methods are considered, namely Encrypt-and-MAC, MAC-then-encrypt, and Encrypt-then-MAC. For each of these and for each notion of security, we indicate whether or not the resulting scheme meets the notion in question assuming that the given symmetric encryption scheme is secure against chosen-plaintext attack and the given MAC is unforgeable under chosen-message attack. We provide proofs for the cases where the answer is “yes” and counter-examples for the cases where the answer is “no.”

/pdf/authenticated-encryption-relations-among-notions-and-4s8vvjvgpy.pdf

Authenticated Encryption: Relations among Notions and Analysis of the Generic Composition Paradigm

We formally study the notion of a joint signature and encryption in the public-key setting. We refer to this primitive as signcryption, adapting the terminology of [35]. We present two definitions for the security of signcryption depending on whether the adversary is an outsider or a legal user of the system. We then examine generic sequential composition methods of building signcryption from a signature and encryption scheme. Contrary to what recent results in the symmetric setting [5, 22] might lead one to expect, we show that classical "encryptthen-sign" (?tS) and "sign-then-encrypt" (St?) methods are both secure composition methods in the public-key setting.We also present a new composition method which we call "commit-thenencrypt-and-sign" (Ct?&S). Unlike the generic sequential composition methods, Ct?&S applies the expensive signature and encryption operations in parallel, which could imply a gain in efficiency over the StE and EtS schemes. We also show that the new Ct?&S method elegantly combines with the recent "hash-sign-switch" technique of [30], leading to efficient on-line/off-line signcryption.Finally and of independent interest, we discuss the definitional inadequacy of the standard notion of chosen ciphertext (CCA2) security. We suggest a natural and very slight relaxation of CCA2-security, which we call generalized CCA2-security (gCCA2). We show that gCCA2-security suffices for all known uses of CCA2-secure encryption, while no longer suffering fromthe definitional shortcomings of the latter.

/pdf/on-the-security-of-joint-signature-and-encryption-37qck37yjb.pdf

On the Security of Joint Signature and Encryption

We introduce a new cryptographic primitive we call concealment, which is related, but quite different from the notion of commitment. A concealment is a publicly known randomized transformation, which, on inputm, outputs a hider h and a binder b. Together, h and b allow one to recoverm, but separately, (1) the hider h reveals “no information” about m, while (2) the binder b can be “meaningfully opened” by at most one hider h. While setting b = m, h = ∅ is a trivial concealment, the challenge is to make |b| |m|, which we call a “non-trivial” concealment. We show that non-trivial concealments are equivalent to the existence of collision-resistant hash functions. Moreover, our construction of concealments is extremely simple, optimal, and yet very general, giving rise to a multitude of efficient implementations. We show that concealments have natural and important applications in the area of authenticated encryption. Specifically, let AE be an authenticated encryption scheme (either publicor symmetric-key) designed to work on short messages. We show that concealments are exactly the right abstraction allowing one to use AE for encrypting long messages. Namely, to encrypt “long” m, one uses a concealment scheme to get h and b, and outputs authenticated ciphertext 〈AE(b), h〉. More surprisingly, the above paradigm leads to a very simple and general solution to the problem of remotely keyed (authenticated) encryption (RKAE) [12, 13]. In this problem, one wishes to split the task of high-bandwidth authenticated encryption between a secure, but low-bandwidth/computationally limited device, and an insecure, but computationally powerful host. We give formal definitions for RKAE, which we believe are simpler and more natural than all the previous definitions. We then show that our composition paradigm satisfies our (very strong) definition. Namely, for authenticated encryption, the host simply sends a short value b to the device (which stores the actual secret key for AE), gets back AE(b), and outputs 〈AE(b), h〉 (authenticated decryption is similar). Finally, we also observe that the particular schemes of [13, 18] are all special examples of our general paradigm.

Concealment and its applications to authenticated encryption

/pdf/on-the-security-of-joint-signature-and-encryption-ipp8c5pajs.pdf

On the Security of Joint Signature and Encryption.

We formally study the notion of a joint signature and encryption in the public-key setting. We refer to this primitive as signcryption, adapting the terminology of [35]. We present two definitions for the security of signcryption depending on whether the adversary is an outsider or a legal user of the system. We then examine generic sequential composition methods of building signcryption from a signature and encryption scheme. Contrary to what recent results in the symmetric setting [5,22] might lead one to expect, we show that classical encrypt-then-sign (£tS) and sign-then-encrypt (Ste) methods are both secure composition methods in the public-key setting. We also present a new composition method which we call commit-then-encrypt-and-sign (Cte&S). Unlike the generic sequential composition methods, CtE&S applies the expensive signature and encryption operations in parallel, which could imply a gain in efficiency over the St£ and etS schemes. We also show that the new Cte&S method elegantly combines with the recent hash-sign-switch technique of [30], leading to efficient on-line/off-line signcryption. Finally and of independent interest, we discuss the definitional inadequacy of the standard notion of chosen ciphertext (CCA2) security. We suggest a natural and very slight relaxation of CCA2-security, which we call generalized CCA2-security (gCCA2). We show that gCCA2-security suffices for all known uses of CCA2-secure encryption, while no longer suffering from the definitional shortcomings of the latter.

On the security of joint signature and encryption

Signcryption is a cryptographic primitive designed to simultaneously provide confidentiality and integrity protection in a communication (see Chap. 1 for a more detailed description of the role of signcryption in a communication architecture ). It is a public-key primitive and can be viewed as the public-key version of the symmetric-key primitive known as authenticated encryption ; indeed, the two primitives share many similarities at a high level.

Jee Hea An

Papers

On the Security of Joint Signature and Encryption

Concealment and its applications to authenticated encryption

On the Security of Joint Signature and Encryption.

On the security of joint signature and encryption

Security for Signcryption: The Two-User Model