On the Pseudorandomness of the Liouville Function of Polynomials over a Finite Field

We study several pseudorandom properties of the Liouville function and the Möbius function of polynomials over a finite field. More precisely, we obtain bounds on their balancedness as well as their well-distribution measure, correlation measure, and linear complexity profile.

On the use of expansion series for stream ciphers

From power series expansions of functions on curves over finite fields, one can obtain sequences with perfect or almost perfect linear complexity profile. It has been suggested by various authors to use such sequences as key streams for stream ciphers. In this work, we show how long parts of such sequences can be computed efficiently from short ones. Such sequences should therefore be considered to be cryptographically weak. Our attack leads in a natural way to a new measure of the complexity of sequences which we call expansion complexity.

Comparison Analysis Of Stream Cipher Algorithms For Digital Communication

Penghantaran maklumat dalam sistem komunikasi radio seperti frekuensi tinggi akan mendedahkan maklumat itu kepada pihak–pihak yang tidak berkaitan. Untuk memastikan maklumat tersebut selamat, ia haruslah dienkodkan terlebih dahulu sebelum dihantar. Bagi maklumat bersaiz besar, pengenkod jenis satu bit adalah lebih sesuai berbanding pengenkod jenis blok kerana ia lebih cepat dan tidak mempengaruhi bit bersebelahan jika berlakunya kesilapan semasa penghantaran. Pengenkod satu bit biasanya dihasilkan menggunakan kaedah anjakan balik secara linear dan juga penggabungan secara tidak linear. Dengan menggunakan panjang kunci yang sama untuk setiap pengenkod iaitu 64 bit, kekuatan pengenkod ditentukan dengan menggunakan beberapa jenis ujian piawaian. Pengenkod yang melepasi kesemua ujian adalah yang paling baik dan sesuai untuk digunakan dalam penghantaran maklumat digital. Kata kunci: Penghantaran, pengenkod, komunikasi, selamat, linear The broadcast nature of radio communication such as in the HF (High Frequency) spectrum exposes the transmitted information to unauthorized third parties. Confidentiality is ensured by employing cipher system. For bulk transmission of data, stream ciphers are ideal choices over block ciphers due to faster implementation speed and not introducing error propagation. The stream cipher algorithms evaluated are based on the linear feedback shift register (LFSR) with nonlinear combining function. By using a common key length and worst case conditions, the strength of several stream cipher algorithms are evaluated using statistical tests, correlation attack, linear complexity profile and nonstandard test. The best algorithm is the one that exceeds all of the tests. Key words: Confidential, LFSR, stream, block, correlation