The stream cipher TPypy has been designed by Biham and Seberry in January 2007 as the strongest member of the Py-family of stream ciphers. At Indocrypt 2007, Sekar, Paul and Preneel showed related-key weaknesses in the Py-family of stream ciphers including the strongest member TPypy. Furthermore, they modified the stream ciphers TPypy and TPy to generate two fast ciphers, namely RCR-32 and RCR-64, in an attempt to rule out all the attacks against the Py-family of stream ciphers. So far there exists no attack on RCR-32 and RCR-64. In this paper, we show that the related-key weaknesses can be still used to construct related-key distinguishing attacks on all Py-family of stream ciphers including the modified versions RCR-32 and RCR-64. Under related keys, we show distinguishing attacks on RCR-32 and RCR-64 with data complexity 2139.3 and advantage greater than 0.5. We also show that the data complexity of the distinguishing attacks on Py-family of stream ciphers proposed by Sekar et al. can be reduced fromto. These results constitute the best attacks on the strongest members of the Py-family of stream ciphers Tpypy, RCR-32 and RCR-64. By modifying the key setup algorithm, we propose two new stream ciphers TRCR-32 and TRCR-64 which are derived from RCR-32 and RCR-64 respectively. Based on our security analysis, we conjecture that no attacks lower than brute force are possible on TRCR-32 and TRCR-64 stream ciphers.
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