Implementing Cryptographic Primitives in the Symbolic Model

When discussing protocol properties in the symbolic (DolevYao; term-based) model of cryptography, the set of cryptographic primitives is defined by the constructors of the term algebra and by the equational theory on top of it. The set of considered primitives is not easily modifiable during the discussion. In particular, it is unclear what it means to define a new primitive from the existing ones, or why a primitive in the considered set may be unnecessary because it can be modeled using other primitives. This is in stark contrast to the computational model of cryptography where the constructions and relationships between primitives are at the very foundation of the theory. In this paper, we explore how a primitive may be constructed from other primitives in the symbolic model, such that no protocol breaks if an atomic primitive is replaced by the construction. As an example, we show the construction of (symbolic) “randomized” symmetric encryption from (symbolic) one-way functions and exclusive or.