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Lecture notes in computer science

Modeling Computational Security in Long-Lived Systems

Ran Canetti, Ling Cheung A, Dilsun Kaynar, Nancy Ann Lynch, Olivier Pereira

Published Jan 1, 2008• 11 citations
Publisher
DOI
10.1007/978-3-540-85361-9_12

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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.

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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. 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
This chapter introduces the Mosca Model, a time-based framework developed by quantum computing pioneer Michele Mosca to help organizations assess their exposure to quantum threats. By comparing three critical variables – how long data must remain secure (Y), how long it will take to migrate to quantum-safe systems (X), and how long until quantum computers can break current encryption (Z) – the model provides a simple inequality (X + Y > Z) that reframes quantum readiness as a race against time. If the sum of X and Y exceeds Z, the organization is already vulnerable, even if Q-Day has not yet arrived. The chapter walks readers through practical applications of the model across various sectors, including finance, healthcare, government, and critical infrastructure. It explores how long-lived data retention requirements and the complexity of cryptographic migration – especially for embedded systems, OT/ICS, and third-party dependencies – can significantly extend X and Y beyond safe thresholds. The discussion includes guidance on how to apply the model using established risk frameworks such as FAIR, NIST RMF, ISO 27005, and DoCRA, and highlights the strategic value of early action to avoid cascading failures in digital trust, compliance, and operational continuity.