F-FCSR Stream Ciphers

Feedback with Carry Shift Registers (FCSRs) are a promising alternative to Linear Feedback Shift Registers (LFSRs) for the design of stream ciphers. The main difference between these two automata lies in the computation of the feedback. While LFSRs use simple bitwise addition, FCSRs use addition with carries. Hence, the transition function of an FCSR is non-linear, more precisely quadratic. Since FCSRs were introduced by Goresky and Klapper [11], the properties of the sequences generated by an FCSR are now considered well mastered from a mathematical point of view. FCSR can help to solve the problem which is always raised when using LFSR. In LFSR-based stream ciphers, a filtering or combining Boolean function must be used to break the linearity of LFSR. With FCSR-based stream ciphers, this issue is directly solved by the intrinsic non-linearity of the FCSR. Thus, a linear filter can be used to extract the keystream from the internal state. Moreover, sequences obtained from an FCSR have the same suitable statistical properties of LFSR sequences: known period, balancedness, equal distribution of patterns. . . We present in this chapter two designs based on filtered FCSR (FFCSR) which are dedicated to hardware applications. F-FCSR-H is our first proposition which fulfill the requirement of eSTREAM profile 2: 80 bits of key and 80 bits of IV. A second proposition, F-FCSR-16, is similar to F-FCSR-H, but uses larger keys and IVs (128 bits for the key and 128 bits for the IV).