Since the linear structure of linear feedback shift registers (LFSRs) has a drawback that may lead to attacks against LFSR-based stream ciphers, feedback with carry shift registers (FCSRs) have been proposed as an alternative to LFSRs for the design of stream ciphers. However, some weaknesses in stream ciphers based on Fibonacci or Galois FCSRs have been exposed. Then, a new ring FCSRs has been proposed which is based on a matrix definition. This new approach generalizes Galois and Fibonacci FCSRs, and circumvents some of their severe weaknesses. In this paper, we give an affirmative answer to the following conjecture: for any given connection integer there exists a ternary transition matrix with a critical path of length 1 and fan-out of 2. We also give an algorithm to construct such transition matrices with given connection integer.

Cloud computing is an emerging computing paradigm in which IT resources and capacities are provided as services over the Internet. It also brings forth new challenges for security when clients want to securely outsource the computation of operations to the untrusted cloud servers. In cloud computing, it is difficult to implement most of cryptographic protocols among clients for this reason that all clients are possibly weaker than computationally powerful players. Hence, clients have to appeal to cloud servers for assistance. However, cloud servers are untrusted so that cryptographic protocols cannot be realized securely. In this paper, we design a secure key agreement scheme for two weaker clients who delegate cloud server to compute modular exponentiation. In our scheme, two clients can get same key for symmetric cryptosystem even that cloud server is untrusted.

In this correspondence, first we give a decomposition of symmetric Boolean functions, then we show that almost all symmetric Boolean functions, including these functions with good algebraic immunity, behave badly against fast algebraic attacks. Besides, we improve the relations between algebraic degree and algebraic immunity of symmetric Boolean functions.

A VLSI design for computing exponentiation in finite fields is developed. An algorithm to generate a relatively long pseudorandom number sequence is presented. It is shown that the period of this sequence is significantly increased compared to that of the sequence generated by the most commonly used maximal length shift register scheme.>