Analysis of NORX: Investigating Differential and Rotational Properties



This paper presents a thorough analysis of the AEAD scheme NORX, focussing on
differential and rotational properties. We first introduce mathematical models
that describe differential propagation with respect to the non-linear operation
of NORX. Afterwards, we adapt a framework previously proposed for ARX designs
allowing us to automatise the search for differentials and characteristics. We
give upper bounds on the differential probability for a small number of steps of
the NORX core permutation. For example, in a scenario where an attacker can only
modify the nonce during initialisation, we show that characteristics have
probabilities of less than $2^{-60}$ ($32$-bit) and $2^{-53}$ ($64$-bit) after
only one round. Furthermore, we describe how we found the best characteristics
for four rounds, which have probabilities of $2^{-584}$ ($32$-bit) and
$2^{-836}$ ($64$-bit), respectively. Finally, we discuss some rotational
properties of the core permutation which yield some first, rough bounds and can
be used as a basis for future studies.


NORX, AEAD, LRX, differential cryptanalysis, rotational cryptanalysis


Latincrypt 2014 2014

Cited by

Year 2015 : 2 citations

 Stefan Kölbl, Gregor Leander , Tyge Tiessen. "Observations on the SIMON Block Cipher Family." In Advances in Cryptology -- CRYPTO 2015 - 35th Annual Cryptology Conference, Santa Barbara, CA, USA, August 16-20, 2015, Proceedings, Part I.

 Sourav Das and Subhamoy Maitra and Willi Meier. "Higher Order Differential Analysis of NORX." Cryptology ePrint Archive, Report 2015/186, 2015.

Year 2014 : 4 citations

 Jean-Philippe Aumasson and Phillip Jovanovic and Samuel Neves. "NORX: Parallel and Scalable AEAD." In Computer Security - ESORICS 2014 - 19th European Symposium on Research in Computer Security, Wroclaw, Poland, September 7-11, 2014.

 Aleksandar Kircanski, "Analysis of Boomerang Differential Trails via a SAT-Based Constraint Solver URSA",, 2014.

 Martin Stanek, "Experimenting with Shuffle Block Cipher and SMT Solvers",, 2014.

 Siwei Sun, Lei Hu, Meiqin Wang, Peng Wang, Kexin Qiao, Xiaoshuang Ma, Danping Shi, Ling Song, Kai Fu. "Towards Finding the Best Characteristics of Some Bit-oriented Block Ciphers and Automatic Enumeration of (Related-key) Differential and Linear Characteristics with Predefined Properties." Cryptology ePrint Archive, Report 2014/747, 2014.