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Journal of the Korea Industrial Information Systems Research

Universal Composability Notion for Functional Encryption Schemes

Sadikin Rifki, Youngho Park, Kil-houm Park, SangJae Moon

Published Jun 30, 2013• 2 citations
Publisher

Abstract

We have developed an ideal functionality for security requirement of functional encryption schemes. The functionality is needed when we want to show the security of a functional encryption scheme in universal composable (UC) framework. A functionality $F_{fe}$ was developed to represent ideal respond of a functional encryption scheme against any polynomial time active attacker. We show that UC security notion of functional encryption scheme $F_{fe}$ is as strong as fully secure functional encryption in an indistinguishable game with chosen cipher text attack. The proof used a method that showing for any environment algorithm, it can not distinguish ideal world where the attacker play with ideal functionality $F_{fe}$ and real world where the attacker play a fully secure functional encryption scheme.

DOI
10.9723/jksiis.2013.18.3.017

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We have developed an ideal functionality for security requirement of functional encryption schemes. The functionality is needed when we want to show the security of a functional encryption scheme in universal composable (UC) framework. A functionality FfeF_{fe}Ffe​ was developed to represent ideal respond of a functional encryption scheme against any polynomial time active attacker. We show that UC security notion of functional encryption scheme FfeF_{fe}Ffe​ is as strong as fully secure functional encryption in an indistinguishable game with chosen cipher text attack. The proof used a method that showing for any environment algorithm, it can not distinguish ideal world where the attacker play with ideal functionality FfeF_{fe}Ffe​ and real world where the attacker play a fully secure functional encryption scheme.
We propose a modification to the framework of Universally Composable (UC) security [3]. Our new notion involves comparing the real protocol execution with an ideal execution involving ideal functionalities (just as in UC-security), but allowing the environment and adversary access to some super-polynomial computational power. We argue the meaningfulness of the new notion, which in particular subsumes many of the traditional notions of security. We generalize the Universal Composition theorem of [3] to the new setting. Then under new computational assumptions, we realize secure multi-party computation (for static adversaries) without a common reference string or any other set-up assumptions, in the new framework. This is known to be impossible under the UC framework.
We propose a modification to the framework of Universally Composable (UC) security [3]. Our new notion, involves comparing the protocol executions with an ideal execution involving ideal functionalities (just as in UC-security), but allowing the environment and adversary access to some super-polynomial computational power. We argue the meaningfulness of the new notion, which in particular subsumes many of the traditional notions of security. We generalize the Universal Composition theorem of [3] to the new setting. Then under new computational assumptions, we realize secure multi-party computation (for static adversaries) without a common reference string or any other set-up assumptions, in the new framework. This is known to be impossible under the UC framework. 1
Identity-based encryption (IBE) is one of the most important primitives in cryptography, and various security notions of IBE (e. g., IND-ID-CCA2, NM-ID-CCA2, IND-sID-CPA etc.) have been introduced. The relations among them have been clarified recently. This paper, for the first time, investigates the security of IBE in the universally composable (UC) framework. This paper first defines the UC-security of IBE, i. e., we define the ideal functionality of IBE, FIBE. We then show that UC-secure IBE is equivalent to conventionally-secure (IND-ID-CCA2-secure) IBE.
The Universal Composability (UC) framework provides provable security guaranties for harsh application environment, where we want to construct protocols which keep security guarantees even when they are concurrently composed with arbitrary number of arbitrary (even hostile) protocols.This is a very strong guarantee.The UC-framework inherently supports the modular design, which allows secure composition of arbitrary number of UC-secure components with an arbitrary protocol.In contrast, traditional analysis and design is a stand alone analysis where security of a single instance is considered, i.e. an instance which is not in potential interaction with any concurrent instances.Furthermore, a typical traditional analysis is informal, i.e. without a formal proof.In spite of these facts, beyond the task of key-exchange this technology have not really took the attention of the community of applied cryptography.From practitioner's point of view the UC-world may seem more or less an academic interest of theoretical cryptographers.Accordingly we take a pragmatic approach, where we concentrate on meaningful compromises between the assumed adversarial strength, ideality wishes and realization complexity while keeping provable security guarantees within the UC-framework.We believe that even modest but provable goals (especially, if tunable to application scenarios) are interesting if a wider penetration of the UC-technology is desired into the daily-practice of protocol applications.
In functional encryption (FE) a sender, Alice, encrypts plaintexts for which a receiver, Bob, can obtain functional evaluations, while Charlie is responsible for initializing the encryption keys and issuing the decryption keys. Standard notions of security for FE deal with a malicious Bob and guarantee the confidentiality of Alice's messages despite the leakage that occurs due to the functional keys that are revealed to the adversary via various forms of indistinguishability experiments that correspond to IND-CPA, IND-CCA and simulation-based security.In this work we provide a complete and systematic investigation of Consistency, a natural security property for FE, that deals with attacks that can be mounted by Alice, Charlie or a collusion of the two against Bob. We develop three main types of consistency notions according to which set of parties is corrupted and investigate their relation to the standard security properties of FE. To validate our different consistency types, we extend the universally composable framework for FE by Matt and Maurer (CSF 2015) and we show that our consistency notions naturally complement FE security by proving how they imply (and are implied by) UC security depending on which set of parties is corrupted; in this way we demonstrate a complete characterization of consistency for FE. Finally, we provide explicit constructions that achieve consistency efficiently either directly via a construction based on MDDH for specific function classes of inner products over a modulo group or generically for all the consistency types via compilers using standard cryptographic tools.
The universal composability (UC) framework enables the modular design of cryptographic protocols by allowing arbitrary compositions of lower-level building blocks. Public-key encryption is unarguably a very important such building block. However, so far no UC-functionality exists that offers non-interactive encryption necessary for modular protocol construction. We provide an ideal functionality for non-committing encryption (i.e., public-key encryption secure against adaptive corruptions) with locally generated, and therefore non-interactive, ciphertexts. As a sanity check, we also provide a property-based security notion that we prove to be equivalent to the UC notion. We then show that the encryption scheme of Camenisch et al. (SCN '16) based on trapdoor permutations securely implements our notion in the random-oracle model without assuming secure erasures. This is the best one can hope to achieve as standard-model constructions do not exist due to the uninstantiability of round-optimal adaptively secure message transfer in the standard model (Nielsen, Crypto '02). We illustrate the modular reusability of our functionality by constructing the first non-interactive signcryption scheme secure against adaptive corruptions without secure erasures in the UC framework.