In this paper, we describe the families of block ciphers named SHipher. We show a symmetric encryption framework based on the SubSet-Sum problem. This framework can provide families of secure, flexible, and any-size block ciphers. We have extensively cryptanalyzed our encryption framework. We can easily control the computational cost by a key selection. Also, this framework offers excellent performance and it is flexible and general enough to admit a variety of implementations on different non-Abelian groups. In this paper, we provide one implementation using a group of matrices whose determinants are 1. This implementation accepts any block size satisfying $3l-1$. If $l=21$, the block size is 62 bits, which suits for full spectrum of lightweight applications. While if $l=341$, the block size is 1022, which provides high security level up to resistant $2^{684}$ differential-attack effort and $2^{1022}$ brute-force attack effort.
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