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Performance of algebraic graphs based stream-ciphers using large finite fields. (English) Zbl 1284.94118

Summary: 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 \(F_q\) or commutative ring \(K\). For practical implementations the most convenient fields are \(F\) and rings modulo \(Z\) modulo \(2^m\). 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.

MSC:

94A60 Cryptography
05C90 Applications of graph theory
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
68W30 Symbolic computation and algebraic computation
94B05 Linear codes (general theory)
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