Performance of algebraic graphs based stream-ciphers using large finite fields

Algebraic graphs D(n, q) and their analog graphs D(n, K), where K is a finite commutative ring were used successfully in Coding Theory (as Tanner graphs for the construction of LDPC codes and turbo-codes) and in Cryptography (stream-ciphers, public-keys and tools for the key-exchange protocols. Many properties of cryptography algorithms largely depend on the choice of finite field Fq or commutative ring K. For practical implementations the most convenient fields are F and rings modulo Z modulo 2m. In this paper the reader can find the first results about the comparison of D(n, 2m) based stream-ciphers for m = 8, 16, 32 implemented in C++. They show that performance (speed) of algorithms gets better when m is increased.