Designs, Codes and Cryptography

, Volume 87, Issue 2–3, pp 225–247 | Cite as

Differential attacks: using alternative operations

  • Roberto CivinoEmail author
  • Céline Blondeau
  • Massimiliano Sala
Part of the following topical collections:
  1. Special Issue: Coding and Cryptography


Is it possible that a block cipher apparently immune to classical differential cryptanalysis can be attacked considering a different operation on the message space? Recently Calderini and Sala showed how to effectively compute alternative operations on a vector space which can serve as message space for a block cipher such that the resulting structure is still a vector space. The latter were used to mount a linearisation attack against a toy cipher. Here we investigate how alternative operations interact with the layers of a substitution–permutation network and show how they influence the differential probabilities, when the difference taken into consideration is different from the usual bit-wise addition modulo two. Furthermore, we design a block cipher which appears to be secure with respect to classical differential cryptanalysis, but weaker with respect to our attack which makes use of alternative operations.


Block ciphers Differential cryptanalysis Distinguisher Alternative operations 

Mathematics Subject Classification

20B35 94A60 68P25 



Roberto Civino thankfully acknowledges support by the Department of Mathematics of the University of Trento and by COST Action IC1306. Roberto Civino and Massimiliano Sala are grateful to MIUR-Italy for financial support via PRIN 2015TW9LSR “Group theory and applications”.


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Authors and Affiliations

  1. 1.University of L’Aquila, DISIML’AquilaItaly
  2. 2.School of ScienceAalto UniversityEspooFinland
  3. 3.Department of MathematicsUniversity of TrentoTrentoItaly

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