基于单向陷门置换的长消息签密方案

在随机Oracle模型的基础上, 提出一种基于单向陷门置换（trapdoor permutations, TDPs）的、可并行的、长消息签密方案——PLSC （parallel long-message signcryption）. 该方法采用“整体搅乱, 局部加密（scramble all, and encrypt small）”的思想, 用一个伪随机数对要传送的消息和用户的身份（ID）进行“搅乱（scrambling operation）”, 然后对两个固定长度的小片段（并行地）进行单向陷门置换（TDP）操作. 这种设计使得整个方案可直接高效地处理任意长度的消息, 既可避免循环调用单向陷门置换（如CBC模式）所造成的计算资源的极度消耗, 也可避免由“对称加密方案”与“签密方案”进行“黑盒混合（black-box hybrid）”所造成的填充（padding）冗余. 不仅可以显著地节约消息带宽, 而且可以显著地提高整体效率. 具体地说, 该方法对任何长度的消息进行签密, 仅需进行一次接收方的TDP运算（相当于加密）, 以及一次发送方的TDP运算（相当于签名）, 从而最大限度地降低了TDP运算的次数, 提高了整体的运算效率. 因为, 对于公钥加密算法来说, 运算量主要集中在TDP运算上, TDP运算是整个算法的瓶颈所在. 另一方面, 由于避免了填充上的冗余, 新方案的效率也高于标准的“黑盒混合”方案.重要的是, 新方案能够达到选择密文攻击下的紧致的语义安全性（IND- CCA2）、密文完整性（INT-CTXT）以及不可否认性（non-repudiation）. 而且所有这些安全要求都可以在多用户（multi-user）、内部安全（insider-security）的环境下得以实现. 另外, 尽管新方案主要针对长消息的签密, 但它也可应用于某些不能进行大块数据处理的环境（智能卡或其他只有少量内存的环境）. 也就是说, 对于这些小内存设备来说, 仍然可以用该方案来实现长消息的签密处理.

Shrinking the keys of discrete-log-type lossy trapdoor functions

To this day, realizations in the standard-model of (lossy) trapdoor functions from discrete-log-type assumptions require large public key sizes, e.g., about Θ(λ 2) group elements for a reduction from the decisional Diffie-Hellman assumption (where λ is a security parameter). We propose two realizations of lossy trapdoor functions that achieve public key size of only Θ(λ) group elements in bilinear groups, with a reduction from the decisional Bilinear Diffie-Hellman assumption. Our first construction achieves this result at the expense of a long common reference string of Θ(λ 2) elements, albeit reusable in multiple LTDF instantiations. Our second scheme also achieves public keys of size Θ(λ), entirely in the standard model and in particular without any reference string, at the cost of a slightly more involved construction. The main technical novelty, developed for the second scheme, is a compact encoding technique for generating compressed representations of certain sequences of group elements for the public parameters.

Ideal secret sharing schemes from permutations

The work presents a new method for the design of ideal secret sharing. The method uses regular mappings that are well suited for construction of perfect secret sharing. The restriction of regular mappings to permutations gives a convenient tool for investigation of the relation between permutations and ideal secret sharing generated by them.

On Additive Combinatorics of Permutations of Z(n)

Let Z(n) denote the ring of integers modulo n. A permutation of Z(n) is a sequence of n distinct elements of Z(n). Addition and subtraction of two permutations is defined element-wise. In this paper we consider two extremal problems on permutations of Z(n), namely, the maximum size of a collection of permutations such that the sum of any two distinct permutations in the collection is again a permutation, and the maximum size of a collection of permutations such that no sum of two distinct permutations in the collection is a permutation. Let the sizes be denoted by s (n) and t (n) respectively. The case when n is even is trivial in both the cases, with s (n) = 1 and t (n) = n!. For n odd, we prove (n phi(n))/2(k) <= s(n) <= n!.2(-)(n-1)/2/((n-1)/2)! and 2 (n-1)/2 . (n-1/2)! <= t (n) <= 2(k) . (n-1)!/phi(n), where k is the number of distinct prime divisors of n and phi is the Euler's totient function.

An R package for permutations, Mallows and Generalized Mallows models

[EN]Probability models on permutations associate a probability value to each of the permutations on n items. This paper considers two popular probability models, the Mallows model and the Generalized Mallows model. We describe methods for making inference, sampling and learning such distributions, some of which are novel in the literature. This paper also describes operations for permutations, with special attention in those related with the Kendall and Cayley distances and the random generation of permutations. These operations are of key importance for the efficient computation of the operations on distributions. These algorithms are implemented in the associated R package. Moreover, the internal code is written in C++.

Optical two-dimensional SW-banyan network: Optical implementation, routing control, and determination of permissible permutations

A 2-D SW-banyan network is introduced by properly folding the 1-D SW-banyan network, and its corresponding optical setup is proposed by means of polarizing beamsplitters and 2-D phase spatial light modulators. Then, based on the characteristics and the proposed optical setup, the control for the routing path between any source-destination pair is given, and the method to determine whether a given permutation is permissible or not is discussed. Because the proposed optical setup consists of only optical polarization elements, it is compact in structure, its corresponding energy loss and crosstalk are low, and its corresponding available number of channels is high. (C) 1996 Society of Photo-Optical Instrumentation Engineers.

Maxwell's Demon, Rectifiers, and the Second Law: Computer Simulation of Smoluchowski's Trapdoor

We have simulated numerically an automated Maxwell's demon inspired by Smoluchowski's ideas of 1912. Two gas chambers of equal area are connected via an opening that is covered by a trapdoor. The trapdoor can open to the left but not to the right, and is intended to rectify naturally occurring variations in density between the two chambers. Our results confirm that though the trapdoor behaves as a rectifier when large density differences are imposed by external means, it can not extract useful work from the thermal motion of the molecules when left on its own.

Clones de constantes et de permutations et leur intervalle monoïdal

Thèse diffusée initialement dans le cadre d'un projet pilote des Presses de l'Université de Montréal/Centre d'édition numérique UdeM (1997-2008) avec l'autorisation de l'auteur.

Inclusive Education, Person-Centered Planning & Systems Change Challenging Permutations and Opportunities

Resumen basado en el de la publicaci??n

Bit-index sort: a fast non-comparison integer sorting algorithm for permutations

This paper describes a fast integer sorting algorithm, herein referred as Bit-index sort, which is a non-comparison sorting algorithm for partial per-mutations, with linear complexity order in execution time. Bit-index sort uses a bit-array to classify input sequences of distinct integers, and exploits built-in bit functions in C compilers supported by machine hardware to retrieve the ordered output sequence. Results show that Bit-index sort outperforms in execution time to quicksort and counting sort algorithms. A parallel approach for Bit-index sort using two simultaneous threads is included, which obtains speedups up to 1.6.

Permutations with a distinct difference property

The topic of this paper arose out of a consideration of Costas sequences, which are used in sonar and radar applications. These sequences have the defining property that all differences of elements the same distance apart, are different. Several infinite families of Costas sequences are known; but there are many existence questions for length greater-or-equal to 32. In this article, we restrict ourselves to sequences with the weaker property that all adjacent differences are different. We give a recursive construction for these, as well as building several infinite families.