Modern Cryptography Volume 1

This open access book systematically explores the statistical characteristics of cryptographic systems, the computational complexity theory of cryptographic algorithms and the mathematical principles behind various encryption and decryption algorithms. The theory stems from technology. Based on Shannon's information theory, this book systematically introduces the information theory, statistical characteristics and computational complexity theory of public key cryptography, focusing on the three main algorithms of public key cryptography, RSA, discrete logarithm and elliptic curve cryptosystem. It aims to indicate what it is and why it is. It systematically simplifies and combs the theory and technology of lattice cryptography, which is the greatest feature of this book. It requires a good knowledge in algebra, number theory and probability statistics for readers to read this book. The senior students majoring in mathematics, compulsory for cryptography and science and engineering postgraduates will find this book helpful. It can also be used as the main reference book for researchers in cryptography and cryptographic engineering areas

Modern Cryptography Volume 1

This open access book systematically explores the statistical characteristics of cryptographic systems, the computational complexity theory of cryptographic algorithms and the mathematical principles behind various encryption and decryption algorithms. The theory stems from technology. Based on Shannon's information theory, this book systematically introduces the information theory, statistical characteristics and computational complexity theory of public key cryptography, focusing on the three main algorithms of public key cryptography, RSA, discrete logarithm and elliptic curve cryptosystem. It aims to indicate what it is and why it is. It systematically simplifies and combs the theory and technology of lattice cryptography, which is the greatest feature of this book. It requires a good knowledge in algebra, number theory and probability statistics for readers to read this book. The senior students majoring in mathematics, compulsory for cryptography and science and engineering postgraduates will find this book helpful. It can also be used as the main reference book for researchers in cryptography and cryptographic engineering areas

PABO: Mitigating Congestion via Packet Bounce in Data Center Networks

In today's data center, a diverse mix of throughput-sensitive long flows and delay-sensitive short flows are commonly presented in shallow-buffered switches. Long flows could potentially block the transmission of delay-sensitive short flows, leading to degraded performance. Congestion can also be caused by the synchronization of multiple TCP connections for short flows, as typically seen in the partition/aggregate traffic pattern. While multiple end-to-end transport-layer solutions have been proposed, none of them have tackled the real challenge: reliable transmission in the network. In this paper, we fill this gap by presenting PABO -- a novel link-layer design that can mitigate congestion by temporarily bouncing packets to upstream switches. PABO's design fulfills the following goals: i) providing per-flow based flow control on the link layer, ii) handling transient congestion without the intervention of end devices, and iii) gradually back propagating the congestion signal to the source when the network is not capable to handle the congestion.Experiment results show that PABO can provide prominent advantage of mitigating transient congestions and can achieve significant gain on end-to-end delay

The Congruencex1x2≡x3x4(modp), the Equationx1x2≡x3x4, and Mean Values of Character Sums

AbstractWe obtain the asymptotic formulae ∣B∩V∣=(∣B∣/p)+O(√∣B∣log2p) for the number of solutions of the congruencex1x2≡x3x4(modp) in a box B of arbitrary size and position, andN(B)=(12/π2)B2logB+CB2+O(B19/13log7/13B), withCgiven explicitly, for the number of solutions of the diophantine equationx1x2≡x3x4with 1≤xi≤B. We also obtain the upper bound for fourth order character sum moments, 1/(p−1) ∑χ≠χo∣ ∑a+Bx=a+1χ(x)∣4⪡B2log2p

Energy-Efficient Flow Scheduling and Routing with Hard Deadlines in Data Center Networks

The power consumption of enormous network devices in data centers has emerged as a big concern to data center operators. Despite many traffic-engineering-based solutions, very little attention has been paid on performance-guaranteed energy saving schemes. In this paper, we propose a novel energy-saving model for data center networks by scheduling and routing "deadline-constrained flows" where the transmission of every flow has to be accomplished before a rigorous deadline, being the most critical requirement in production data center networks. Based on speed scaling and power-down energy saving strategies for network devices, we aim to explore the most energy efficient way of scheduling and routing flows on the network, as well as determining the transmission speed for every flow. We consider two general versions of the problem. For the version of only flow scheduling where routes of flows are pre-given, we show that it can be solved polynomially and we develop an optimal combinatorial algorithm for it. For the version of joint flow scheduling and routing, we prove that it is strongly NP-hard and cannot have a Fully Polynomial-Time Approximation Scheme (FPTAS) unless P=NP. Based on a relaxation and randomized rounding technique, we provide an efficient approximation algorithm which can guarantee a provable performance ratio with respect to a polynomial of the total number of flows.Comment: 11 pages, accepted by ICDCS'1