Yingpu Deng

A conjecture about binary strings and its applications on constructing Boolean functions with optimal algebraic immunity

In this paper, a combinatorial conjecture about binary strings is proposed. Under the assumption that the proposed conjecture is correct, two classes of Boolean functions with optimal algebraic immunity can be obtained. The functions in first class are bent, and then it can be concluded that the algebraic immunity of bent functions can take all possible values except one. The functions in the second class are balanced, and they have optimal algebraic degree and the best nonlinearity up to now.

Boolean functions optimizing most of the cryptographic criteria

In this paper, we construct a class of 2 k -variable Boolean functions which have optimal algebraic degree, very high nonlinearity, optimal algebraic immunity, and are 1 -resilient. These properties are unconditional except the algebraic immunity property, which is optimal under some unproven assumptions. However, since the assumptions are verified to be true for k ? 29 , so these functions have optimal algebraic immunity at least for k ? 29 . Highlights? We consider the construction of Boolean functions with good cryptographic properties. ? We construct Boolean functions on even variables which are 1-resilient, with optimal algebraic degree, optimal algebraic immunity and very high nonlinearity. ? We use a combinatorial conjecture about modular addition with carries.

An algebraic broadcast attack against NTRU

In this paper, we propose an algebraic broadcast attack against NTRU, which recovers a single message encrypted multiple times using different NTRU public keys. Namely, when a message is broadcasted, under some reasonable assumptions, our attack can be completed in polynomial time and space. To the best of our knowledge, this is the first successful broadcast attack against NTRU.

New results on nonexistence of generalized bent functions

We obtain two kinds of new results on nonexistence of generalized bent functions (GBFs). Based on the results of Feng, Liu and Ma, we use Schmidt’s field descent method to get the first kind. For the second kind, we use both decomposition law in cyclotomic fields and bent requirements to prove that no GBFs with type

Results on permutation symmetric Boolean functions

[3,\,2\cdot 23^{e}]

A New Attack against the Selvi-Vivek-Rangan Deterministic Identity Based Signature Scheme from ACISP 2012

[3,2·23e] exist.

An algorithm for computing the factor ring of an ideal in Dedekind domain with finite rank

Define ψm to be the smallest strong pseudoprime to the firstm prime bases. The exact value of ψm is known for 1 ≤ m ≤ 8. Z. Zhang have found a 19decimal-digit number Q11 = 3825 12305 65464 13051 which is a strong pseudoprime to the first 11 prime bases and he conjectured that ψ9 = ψ10 = ψ11 = Q11. We prove the conjecture by algorithms.

On orders in number fields: Picard groups, ring class fields and applications

This paper provides a systematic method on the enumeration of various permutation symmetric Boolean functions. The results play a crucial role on the search of permutation symmetric Boolean functions with good cryptographic properties. The proposed method is algebraic in nature. As a by-product, the authors correct and generalize the corresponding results of Stănică and Maitra (2008). Further, the authors give a complete classification of block-symmetric bent functions based on the results of Zhao and Li (2006), and the result is the only one classification of a certain class of permutation symmetric bent functions after the classification of symmetric bent functions proposed by Savicky (1994).