Most computational soundness theorems deal with a limited number of primitives, thereby limiting their applicability. The notion of deduction soundness of Cortier and Warinschi (CCS\'11) aims to facilitate soundness theorems for richer frameworks via composition results: deduction soundness extends, generically, with asymmetric encryption and public data structures. Unfortunately, that paper also hints at rather serious limitations regarding further composition results: composability with digital signatures seems to be precluded.
In this paper we provide techniques for bypassing the perceived limitations of deduction soundness and demonstrate that it enjoys vastly improved composition properties. More precisely, we show that a deduction sound implementation can be modularly extended with all of the basic cryptographic primitives (symmetric/asymmetric encryption, message authentication codes, digital signatures, and hash functions). We thus obtain the first soundness framework that allows for the joint use of multiple instances of all of the basic primitives.
In addition, we show how to overcome an important restriction of the bare deduction soundness framework which forbids sending encrypted secret keys. In turn, this prevents its use for the analysis of a large class of interesting protocols (e.g. key exchange protocols). We allow for more liberal uses of keys as long as they are hidden in a sense that we also define. All primitives typically used to send secret data (symmetric/asymmetric encryption) satisfy our requirement which we also show to be preserved under composition.