Paper 2014/656

Cryptanalytic Time-Memory-Data Tradeoffs for FX-Constructions with Applications to PRINCE and PRIDE

Itai Dinur

Abstract

The FX-construction was proposed in 1996 by Kilian and Rogaway as a generalization of the DESX scheme. The construction increases the security of an $n$-bit core block cipher with a $\kappa$-bit key by using two additional $n$-bit masking keys. Recently, several concrete instances of the FX-construction were proposed, including PRINCE (proposed at Asiacrypt 2012) and PRIDE (proposed at CRYPTO 2014). These ciphers have $n=\kappa=64$, and are proven to guarantee about $127-d$ bits of security, assuming that their core ciphers are ideal, and the adversary can obtain at most $2^d$ data. In this paper, we devise new cryptanalytic time-memory-data tradeoff attacks on FX-constructions, combining recent techniques by Fouque, Joux and Mavromati with time-memory-data tradeoffs for stream ciphers. While our attacks do not contradict the security proof of PRINCE and PRIDE, nor pose an immediate threat to their users, some specific choices of tradeoff parameters demonstrate that the security margin of the ciphers against practical attacks is smaller than expected. Finally, we propose very light changes to PRINCE and PRIDE. These changes ensure that the ciphers resist our attacks while maintaining their design goals, with the exception of the theoretical security proof (which is invalidated, as PRINCE and PRIDE are no longer FX-constructions). Consequently, we conclude that although the FX-construction provides a very simple way of increasing the security of a widely deployed cipher (such as DES at the time), using it for a new design is a less reasonable approach.