International Association
for Cryptologic Research

We give a framework for relating the quantitative, concrete security of a "reference'' protocol (say, one appearing in an academic paper) to that of some derived, "real'' protocol (say, appearing in a cryptographic standard). It is based on the indifferentiability framework of Maurer, Renner, and Holenstein (MRH), whose application has been exclusively focused upon non-interactive cryptographic primitives, e.g., hash functions and Feistel networks. Our extension of MRH is supported by a clearly defined execution model, and two composition lemmata, all formalized in a modern pseudocode language. Together, these allow for precise statements about game-based security properties of cryptographic objects (interactive or not) at various levels of abstraction, As a real-world application, we design and prove tight security bounds for a potential TLS 1.3 extension that integrates the SPAKE2 password-authenticated key-exchange into the existing handshake. (This is a problem of current interest to the IETF.)

Key separation is often difficult to enforce in practice. While key reuse can be catastrophic for security, we know of a number of cryptographic schemes for which it is provably safe. But existing formal models, such as the notions of joint security (Haber-Pinkas, CCS ’01) and agility (Acar et al., EUROCRYPT ’10), do not address the full range of key-reuse attacks—in particular, those that break the abstraction of the scheme, or exploit protocol interactions at a higher level of abstraction. This work attends to these vectors by focusing on two key elements: the game that codifies the scheme under attack, as well as its intended adversarial model; and the underlying interface that exposes secret key operations for use by the game. Our main security experiment considers the implications of using an interface (in practice, the API of a software library or a hardware platform such as TPM) to realize the scheme specified by the game when the interface is shared with other unspecified, insecure, or even malicious applications. After building up a definitional framework, we apply it to the analysis of two real-world schemes: the EdDSA signature algorithm and the Noise protocol framework. Both provide some degree of context separability, a design pattern for interfaces and their applications that aids in the deployment of secure protocols.