Computational Soundness, Co-induction, and Encryption Cycles

  • Daniele Micciancio
Conference paper

DOI: 10.1007/978-3-642-13190-5_19

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6110)
Cite this paper as:
Micciancio D. (2010) Computational Soundness, Co-induction, and Encryption Cycles. In: Gilbert H. (eds) Advances in Cryptology – EUROCRYPT 2010. EUROCRYPT 2010. Lecture Notes in Computer Science, vol 6110. Springer, Berlin, Heidelberg


We analyze the relation between induction, co-induction and the presence of encryption cycles in the context of computationally sound symbolic equivalence of cryptographic expressions. Our main finding is that the use of co-induction in the symbolic definition of the adversarial knowledge allows to prove soundness results without the need to require syntactic restrictions, like the absence of encryption cycles, common to most previous work in the area. Encryption cycles are relevant only to the extent that the key recovery function associated to acyclic expressions can be shown to have a unique fixed point. So, when a cryptographic expression has no encryption cycles, the inductive (least fixed point) and co-inductive (greatest fixed point) security definitions produce the same results, and the computational soundness of the inductive definitions for acyclic expressions follows as a special case of the soundness of the co-inductive definition.


Computational soundness co-induction greatest fixed points formal methods for security symbolic encryption encryption cycles 

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Daniele Micciancio
    • 1
  1. 1.University of California at San DiegoLa JollaUSA

Personalised recommendations