On group properties of classes Source-Heavy and Target-Heavy Feistel block ciphers with round functions linear dependent on round keys parts

Source-Heavy and Target-Heavy block ciphers, which are based on a shift register of length $m \ge 3$ over $GF({2^n})$, are generalized Feistel schemes. Well-known examples of these ciphers are RC2, MARS. In this paper, we study Source-Heavy and Target-Heavy block ciphers such that round functions over a finite abelian group $X$ depend linearly on parts of round keys. We describe conditions on round functions such that a group $G$ generated by round functions is embedded in an exponentiation subgroup. Under these conditions, we get metrics saved by the encryption function for all round keys and $G$.