Abstract. For many cryptographic protocols, security relies on the assumption that adversarial entities have lim-ited computational power. This type of security degrades progressively over the lifetime of a protocol. However, some cryptographic services, such as timestamping services or digital archives, are long-lived in nature; they are expected to be secure and operational for a very long time (i.e., super-polynomial). In such cases, security cannot be guaranteed in the traditional sense: a computationally secure protocol may become insecure if the attacker has a super-polynomial number of interactions with the protocol. This paper proposes a new paradigm for the analysis of long-lived security protocols. We allow entities to be active for a potentially unbounded amount of real time, provided they perform only a polynomial amount of work per unit of real time. Moreover, the space used by these entities is allocated dynamically and must be polynomially bounded. We propose a new notion of long-term implementation, which is an adaptation of computational indistinguishability to the long-lived setting. We show that long-term implementation is preserved under polynomial parallel composi-tion and exponential sequential composition. We illustrate the use of this new paradigm by analyzing some security properties of the long-lived timestamping protocol of Haber and Kamat. 1
Abstract. For many cryptographic protocols, security relies on the assumption that adversarial entities have lim-ited computational power. This type of security degrades progressively over the lifetime of a protocol. However, some cryptographic services, such as timestamping services or digital archives, are long-lived in nature; they are expected to be secure and operational for a very long time (i.e., super-polynomial). In such cases, security cannot be guaranteed in the traditional sense: a computationally secure protocol may become insecure if the attacker has a super-polynomial number of interactions with the protocol. This paper proposes a new paradigm for the analysis of long-lived security protocols. We allow entities to be active for a potentially unbounded amount of real time, provided they perform only a polynomial amount of work per unit of real time. Moreover, the space used by these entities is allocated dynamically and must be polynomially bounded. We propose a new notion of long-term implementation, which is an adaptation of computational indistinguishability to the long-lived setting. We show that long-term implementation is preserved under polynomial parallel composi-tion and exponential sequential composition. We illustrate the use of this new paradigm by analyzing some security properties of the long-lived timestamping protocol of Haber and Kamat. 1
For many cryptographic protocols, security relies on the assumption that adversarial entities have limited computational power. This type of security degrades progressively over the lifetime of a protocol. However, some cryptographic services, such as timestamping services or digital archives, are emph{long-lived} in nature; they are expected to be secure and operational for a very long time (ie super-polynomial). In such cases, security cannot be guaranteed in the traditional sense: a computationally secure protocol may become insecure if the attacker has a super-polynomial number of interactions with the protocol. This paper proposes a new paradigm for the analysis of long-lived security protocols. We allow entities to be active for a potentially unbounded amount of real time, provided they perform only a polynomial amount of work emph{per unit of real time}. Moreover, the space used by these entities is allocated dynamically and must be polynomially bounded. We propose a new notion of emph{long-term implementation}, which is an adaptation of computational indistinguishability to the long-lived setting. We show that long-term implementation is preserved under polynomial parallel composition and exponential sequential composition. We illustrate the use of this new paradigm by analyzing some security properties of the long-lived timestamping protocol of Haber and Kamat.
Abstract. To prove security of a multi-party cryptographic protocol, one often reduces attacks on the protocol to attacks on a suitable computational problem. Thus, if the computational problem is hard, then the protocol is secure. But to allow for a security reduction, the protocol itself and the attack on the protocol must be efficient, i.e., polynomialtime. Of course, the obvious way to enforce an overall polynomial runtime of the protocol is to require each individual protocol machine and adversarial entity to be polynomialtime. However, as the specific case of zero-knowledge protocols demonstrates, an a priori polynomial-time bound on all entities may not be an optimal choice because the running time of some machines needs to depend on that of others. As we want to be able to model arbitrary protocol tasks, we work in the Universal Composability framework (UC). This framework additionally provides strong composability guarantees. We will point out that in the UC setting, finding a useful notion of polynomial-time for the analysis of general protocols is a highly non-trivial task. Our goal in this work is to find a good and useful definition of polynomial-time for multiparty protocols in the UC setting that matches the intuition of what is feasible. A good
We present a general framework for representing cryptographic protocols and analyzing their security. The framework allows specifying the security requirements of practically any cryptographic task in a unified and systematic way. Furthermore, in this framework the security of protocols is preserved under a general protocol composition operation, called universal composition. The proposed framework with its security-preserving composition operation allows for modular design and analysis of complex cryptographic protocols from relatively simple building blocks. Moreover, within this framework, protocols are guaranteed to maintain their security in any context, even in the presence of an unbounded number of arbitrary protocol instances that run concurrently in an adversarially controlled manner. This is a useful guarantee, that allows arguing about the security of cryptographic protocols in complex and unpredictable environments such as modern communication networks.
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.
The study of secure multiparty computation has yielded powerful feasibility results showing that any efficient functionality can be securely computed in the presence of malicious adversaries. Despite this, there are few problems of specific interest for which we have highly efficient protocols that are secure in the presence of malicious adversaries under full simulation based definitions (following the ideal/real model paradigm). Due to the difficulties of constructing such protocols, many researchers have resorted to weaker definitions of security and weaker adversary models. In this paper, we construct highly efficient protocols for the well-studied problem of oblivious polynomial evaluation. Our protocol is secure under standard cryptographic assumptions for the settings of malicious adversaries, and readily transform to protocols that are secure under universal composability and in the presence of covert adversaries. Our protocol is constant round and requires O(d · s) exponentiations, where d is the degree of the polynomial and s is a statistical security parameter (that should equal about 160 in practice).
We address the problem of the-security of cryptographic protocols in face of future advances in computing technology and algorithmic research. The problem stems from the fact may be deemed that computations which at a given point in time may be deemed infeasible, can, in the course of years or decades, be made possible with improved hardware and/or breakthroughs in code-breaking algorithms. In such cases, the security of historical , but nonetheless highly confidential data may be in jeopardy. We present a scheme for efficient secure two-party communication with provable everlasting security. The security is guaranteed in face of any future technological advances, given the current state of of the art. Furthermore, the security of the messages is also guaranteed even if the secret encryption/decryption key is revealed in the future, The scheme is based on the bounded storage model and provides information-theoretic security in this model. The bounded storage model postulates an adversary who is computationally unbounded, and is only bounded in the amount of storage (not computation space) available to store the output of his computation. The bound on the storage can be arbitrarily large (e.g., 100 Tbytes), as long as it is fixed. Given this storage bound, our protocols guarantee that even a computationally all powerful adversary gains no information about a message (except with a probability that is exponentially small in the security parameter k). The bound on storage space need only hold at the time of the message transmission. Thereafter, no additional storage space or, computational power can help the adversary in deciphering the message. We present two protocols. The first protocol, which elaborates on the autoregressive (AR) protocol of Aumann and Rabin (see Advances in Cryptology-Crypto '99, p. 65-79, 1999), employs a short secret key whose size is independent of the length of the message, but uses many public random bits. The second protocol uses an optimal number of public random bits, but employs a longer secret key. Our proof of security utilizes a novel linear algebraic technique.