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

Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/non-Hamiltonian.In this paper a computational complexity theory of the “knowledge” contained in a proof is developed. Zero-knowledge proofs are defined as those proofs that convey no additional knowledge other than the correctness of the proposition in question. Examples of zero-knowledge proof systems are given for the languages of quadratic residuosity and 'quadratic nonresiduosity. These are the first examples of zero-knowledge proofs for languages not known to be efficiently recognizable.

/pdf/the-knowledge-complexity-of-interactive-proof-systems-31apre0ecf.pdf

The knowledge complexity of interactive proof-systems

Cloud computing is an emerging computing paradigm in which resources of the computing infrastructure are provided as services over the Internet. As promising as it is, this paradigm also brings forth many new challenges for data security and access control when users outsource sensitive data for sharing on cloud servers, which are not within the same trusted domain as data owners. To keep sensitive user data confidential against untrusted servers, existing solutions usually apply cryptographic methods by disclosing data decryption keys only to authorized users. However, in doing so, these solutions inevitably introduce a heavy computation overhead on the data owner for key distribution and data management when fine-grained data access control is desired, and thus do not scale well. The problem of simultaneously achieving fine-grainedness, scalability, and data confidentiality of access control actually still remains unresolved. This paper addresses this challenging open issue by, on one hand, defining and enforcing access policies based on data attributes, and, on the other hand, allowing the data owner to delegate most of the computation tasks involved in fine-grained data access control to untrusted cloud servers without disclosing the underlying data contents. We achieve this goal by exploiting and uniquely combining techniques of attribute-based encryption (ABE), proxy re-encryption, and lazy re-encryption. Our proposed scheme also has salient properties of user access privilege confidentiality and user secret key accountability. Extensive analysis shows that our proposed scheme is highly efficient and provably secure under existing security models.

/pdf/achieving-secure-scalable-and-fine-grained-data-access-3h59d4tpb3.pdf

Achieving Secure, Scalable, and Fine-grained Data Access Control in Cloud Computing

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

A system and method for communicating information between a first party and a second party, comprising the steps of receiving, by an intermediary, an identifier of desired information and accounting information for a transaction involving the information from the first party, transmitting an identifier of the first party to the second party, and negotiating, by the intermediary, a comprehension function for obscuring at least a portion of the information communicated between the first party and the second party. The data transmission may be made secure with respect to the intermediary by providing an asymmetric key or direct key exchange for encryption of the communication between the first and second party. The data transmission may be made secure with respect to the second party by maintaining the information in encrypted format at the second party, with the decryption key held only by the intermediary, and transmitting a secure composite of the decryption key and a new encryption key to the second party for transcoding of the data record, and providing the new decryption key to the first party, so that the information transmitted to the first party can be comprehended by it.

System and method for secure three-party communications

First, we introduce the notion of divertibility as a protocol property as opposed to the existing notion as a language property (see Okamoto, Ohta [OO90]) We give a definition of protocol divertibility that applies to arbitrary 2-party protocols and is compatible with Okamoto and Ohta's definition in the case of interactive zero-knowledge proofs Other important examples falling under the new definition are blind signature protocols We propose a sufficiency criterion for divertibility that is satisfied by many existing protocols and which, surprisingly, generalizes to cover several protocols not normally associated with divertibility (eg, Diffie-Hellman key exchange) Next, we introduce atomic proxy cryptography, in which an atomic proxy function, in conjunction with a public proxy key, converts ciphertexts (messages or signatures) for one key into ciphertexts for another Proxy keys, once generated, may be made public and proxy functions applied in untrusted environments We present atomic proxy functions for discrete-log-based encryption, identification, and signature schemes It is not clear whether atomic proxy functions exist in general for all public-key cryptosystems Finally, we discuss the relationship between divertibility and proxy cryptography

/pdf/divertible-protocols-and-atomic-proxy-cryptography-4vwmnv63cy.pdf

Divertible protocols and atomic proxy cryptography

Many eligibility or entitlement certificates in every day life are non-transferable between persons. However, they are usually implemented by personal physical tokens that owners can easily pass around (e.g. credit card), driver’s license). So there must either be negligible incentives to pass these certificates or the tokens around, or the tokens must allow to authenticate the persons who show certificates, e.g., by imprinted photographs. However, any kind of easily accessible personal identifying information threatens the owners’ privacy. To solve these somehow paradoxical requirements, we assume for each owner a kind of pilot that is equipped with a tamper resistant biometric authentication facility. We draft cryptographic protocols for issuing and showing non-transferable yet privacy protecting certificates. Unforgeability of certificates relies on a well-established computational assumption, nontransferability relies upon a physical assumption and owners’ privacy is protected unconditionally.

Biometric yet Privacy Protecting Person Authentication

PC franking systems allow customers to download postage value into their PCs and to print postage value onto envelopes or mailing labels by using regular desktop printers connected to their PCs. In emerging standards, such as the IBIP program of the US postal services, the resulting imprints are called indicia, and they are printed as 2-D bar codes that are easy and reliable to scan while passing through the mail delivery system. In contrast to the IBIP program, which requires a tamper responsive postal security device for each customer, we propose a pure software solution for PC franking systems that is more secure for the postal services, gives more privacy to the customers and has the potential of being much cheaper than any IBIP compliant franking system. In contrast to existing PC-franking products that require no hardware postal security device, our solution works off-line. Customers are not required to be online while printing indicia. Our solution operates an existing offine e-cash scheme over certain elliptic curves rather than over finite fields.

http://dud.inf.tu-dresden.de/sirene/people/gerrit/papers/e-postage.pdf

Gerrit Bleumer

Papers

Divertible protocols and atomic proxy cryptography

Biometric yet Privacy Protecting Person Authentication

Secure PC-Franking for Everyone