The Generic Unwinding Theorem for CSP Noninterference Security

 

Title: The Generic Unwinding Theorem for CSP Noninterference Security
Author: Pasquale Noce (pasquale /dot/ noce /dot/ lavoro /at/ gmail /dot/ com)
Submission date: 2015-06-11
Abstract:

The classical definition of noninterference security for a deterministic state machine with outputs requires to consider the outputs produced by machine actions after any trace, i.e. any indefinitely long sequence of actions, of the machine. In order to render the verification of the security of such a machine more straightforward, there is a need of some sufficient condition for security such that just individual actions, rather than unbounded sequences of actions, have to be considered.

By extending previous results applying to transitive noninterference policies, Rushby has proven an unwinding theorem that provides a sufficient condition of this kind in the general case of a possibly intransitive policy. This condition has to be satisfied by a generic function mapping security domains into equivalence relations over machine states.

An analogous problem arises for CSP noninterference security, whose definition requires to consider any possible future, i.e. any indefinitely long sequence of subsequent events and any indefinitely large set of refused events associated to that sequence, for each process trace.

This paper provides a sufficient condition for CSP noninterference security, which indeed requires to just consider individual accepted and refused events and applies to the general case of a possibly intransitive policy. This condition follows Rushby's one for classical noninterference security, and has to be satisfied by a generic function mapping security domains into equivalence relations over process traces; hence its name, Generic Unwinding Theorem. Variants of this theorem applying to deterministic processes and trace set processes are also proven. Finally, the sufficient condition for security expressed by the theorem is shown not to be a necessary condition as well, viz. there exists a secure process such that no domain-relation map satisfying the condition exists.

BibTeX:
@article{Noninterference_Generic_Unwinding-AFP,
  author  = {Pasquale Noce},
  title   = {The Generic Unwinding Theorem for CSP Noninterference Security},
  journal = {Archive of Formal Proofs},
  month   = jun,
  year    = 2015,
  note    = {\url{http://isa-afp.org/entries/Noninterference_Generic_Unwinding.shtml},
            Formal proof development},
  ISSN    = {2150-914x},
}
License: BSD License
Depends on: Noninterference_Ipurge_Unwinding