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- Miroslav Halás, Ülle Kotta, Ziming Li, Huaifu Wang, Chunming Yuan
- ISSAC
- 2009

The paper describes an algebraic construction of the inversive difference field associated with a discrete-time rational nonlinear control system under the assumption that the system is submersive. We prove that a system is submersive iff its associated difference ideal is proper, prime and reflexive. Next, we show that Kähler differentials of the… (More)

- Yujuan Li, Huaifu Wang, Jinhua Zhao
- IACR Cryptology ePrint Archive
- 2013

In this paper, we give conditions under which the trinomials of the form x n + ax + b over finite field Fpm are not primitive and conditions under which there are no primitive trinomials of the form x n + ax + b over finite field Fpm. For finite field F4, We show that there are no primitive trinomials of the form x n + x + α, if n ≡ 1 mod 3 or n ≡ 0 mod 3… (More)

- Ziming Li, Martin Ondera, Huaifu Wang
- ACCA
- 2009

Let k be a commutative field, σ an automorphism of k, and δ a derivation on k with respect to σ. Ore in [7] defines a (univariate) polynomial ring k[∂; σ, δ], which is called an Ore or skew polynomial ring. An Ore polynomial ring is, in general, noncommutative. Its commutation rule is ∂r = σ(r)∂ + δ(r) for all r ∈ k. For example, C(t)[∂; 1, δ], where 1 maps… (More)

In this note, we present an answer to Exercise 9.3 in the Book Symbolic Integration I (second edition) by M. Bronstein, under an additional assumption that the real elementary extension in the exercise is purely transcendental. Our answer is based on a rather technical lemma derived from a naive attempt to do the exercise inductively.

- Yujuan Li, Jinhua Zhao, Huaifu Wang
- IACR Cryptology ePrint Archive
- 2014

In this paper, we explore the primitivity of trinomials over small finite fields. We extend the results of the primitivity of trinomials x n + ax + b over F4 [1] to the general form x n + ax k + b. We prove that for given n and k, one of all the trinomials x n + ax k + b with b being the primitive element of F4 and a + b = 1 is primitive over F4 if and only… (More)

- Yujuan Li, Wenhua Shen, Huaifu Wang, Peipei Zhou
- IACR Cryptology ePrint Archive
- 2014

Recently, Kalikinkar Mandal and Guang Gong presented a family of nonlinear pseudo-random number generators using Welch-Gong Transformations in their paper [6]. They also performed the cycle decomposition of the WG-NLFSR recurrence relations over different finite fields by computer simulations where the nonlinear recurrence relation is composed of a… (More)

- Ziming Li, Huaifu Wang
- J. Systems Science & Complexity
- 2011

We present a criterion for the similarity of length-two elements in a noncom-mutative principal ideal domain. The criterion enables us to develop an algorithm for determining whether B 1 A 1 and B 2 A 2 are similar, where A 1 , A 2 , B 1 , B 2 are first-order differential (difference) operators. The main step in the algorithm is to find a rational solution… (More)

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