Model and physical implementation of multi-port PUF in 65 nm CMOS

In modern cryptographic systems, multi-port physically unclonable function (MPUF) is an efficient mechanism for many security applications, which extracts secret information inherently embedded in the unclonable physical variations and generates multiple secret keys. In this article, we propose an explicit analytic MPUF model, which is useful in predicting the effect of parameter changes on the state as well as in optimizing the design of PUF. Then, a novel MPUF based on register file is designed and fabricated in TSMC low-power 65?nm CMOS technology. There are four ports in the MPUF, and each port produces a 256-bit key. The chip has an area of 0.045?mm², and has a peak clock frequency of 1.25?GHz at 1.2?V. The average power consumption is 13.8?mW at 27°C. Being multi-ports technology and high operation frequency, the throughput of MPUF improves about 50 times compared to the other works. We carry out a robust test by varying the operational conditions such as supply voltage, temperature and noise. The measured results show that the reliability achieves 98.1% at worse case and has a certain improvement compared with the proposed works. The reliability operates at an acceptable range in integrated circuit identification (ICID).     

基于65nm工艺的高性能低功耗处理器设计

研究并设计一款RISC处理器,从架构设计、电路设计、芯片后端设计多个层次保证其高性能、低功耗的特点.在架构设计层面,通过扩展寄存器堆来提升数据交互的局部性并降低对存储器的访问次数.在电路设计层面,利用动态门控时钟技术对乘除法模块和寄存器堆进行高效的时钟控制.在芯片后端设计层面,分析并比较TSMC 65 nm中GP和LP 2种工艺库,采用多阈值设计流程进一步提高处理器的速度并降低功耗.测试结果表明,与其他平台下的性能结果相比,该处理器可以将RS前向纠错解码算法的吞吐率提高4倍～70倍.     

Coupling of Nonconforming Finite Elements and Boundary Elements I: A Priori Estimates

Nonconforming finite element methods are sometimes considered as a variational crime and so we may regard its coupling with boundary element methods. In this paper, the symmetric coupling of nonconforming finite elements and boundary elements is established and a priori error estimates are shown. The coupling involves a further continuous layer on the interface in order to separate the nonconformity in the domain from its boundary data which are required to be continuous. Numerical examples prove the new scheme useful in practice. A posteriori error control and adaptive algorithms will be studied in the forthcoming Part II. Received: November 26, 1997; revised February 10, 1999     

Variable Additive Preconditioning Procedures

Iterative methods with variable preconditioners of additive type are proposed. The scaling factors of each summand in the additive preconditioners are optimized within each iteration step. It is proved that the presented methods converge at least as fast as the Richardson's iterative method with the corresponding additive preconditioner with optimal scaling factors. In the presented numerical experiments the suggested methods need nearly the same number of iterations as the usual preconditioned conjugate gradient method with the corresponding additive preconditioner with numerically determined fixed optimal scaling factors. Received: June 10, 1998; revised October 16, 1998     

An Optimal Algorithm for Bound and Equality Constrained Quadratic Programming Problems with Bounded Spectrum

An implementation of the recently proposed semi-monotonic augmented Lagrangian algorithm for solving the large convex bound and equality constrained quadratic programming problems is considered. It is proved that if the algorithm is applied to the class of problems with uniformly bounded spectrum of the Hessian matrix, then the algorithm finds an approximate solution at O(1) matrix-vector multiplications. The optimality results are presented that do not depend on conditioning of the matrix which defines the equality constraints. Theory covers also the problems with dependent constraints. Theoretical results are illustrated by numerical experiments.     

Matlab Implementation of the Finite Element Method in Elasticity

A short Matlab implementation for P ₁ and Q ₁ finite elements (FE) is provided for the numerical solution of 2d and 3d problems in linear elasticity with mixed boundary conditions. Any adaptation from the simple model examples provided to more complex problems can easily be performed with the given documentation. Numerical examples with postprocessing and error estimation via an averaged stress field illustrate the new Matlab tool and its flexibility. Received June 18, 2001; revised February 25, 2002 Published online: December 5, 2002     

Uniformly Effective Numerical Methods for Hyperbolic Systems

A unified method to compute compressible and incompressible flows is presented. Accuracy and efficiency do not degrade as the Mach number tends to zero. A staggered scheme solved with a pressure correction method is used. The equation of state is arbitrary. A Riemann problem for the barotropic Euler equations with nonconvex equation of state is solved exactly and numericaly. A hydrodynamic flow with cavitation in which the Mach number varies between 10⁻³ and 20 is computed. Unified methods for compressible and incompressible flows are further discussed for the flow of a perfect gas. The staggered scheme with pressure correction is found to have Mach-uniform accuracy and efficiency, and for the fully compressible case the accuracy is comparable with that of established schemes for compressible flows. Received October 20, 1999; revised May 26, 2000     

Tensor Product Multigrid for Maxwell's Equation with Aligned Anisotropy

When simulating electromagnetic phenomena in symmetric cavities, it is often possible to exploit the symmetry in order to reduce the dimension of the problem, thereby reducing the amount of work necessary for its numerical solution. Usually, this reduction leads not only to a much lower number of unknowns in the discretized system, but also changes the behaviour of the coefficients of the differential operator in an unfavourable way, usually leading to the transformed system being not elliptic with respect to norms corresponding to two-dimensional space, thus limiting the use of standard multigrid techniques. In this paper, we introduce a robust multigrid method for Maxwell's equation in two dimensions that is especially suited for coefficients resulting from coordinate transformations, i.e. that are aligned with the coordinate axes. Using a variant of the technique introduced in [5], we can prove robustness of the multigrid method for domains of tensor-product structure and coefficients depending on only one of the coordinates. Received July 17, 2000; revised October 27, 2000     

Homogenization and Multigrid

For elliptic partial differential equations with periodically oscillating coefficients which may have large jumps, we prove robust convergence of a two-grid algorithm using a prolongation motivated by the theory of homogenization. The corresponding Galerkin operator on the coarse grid turns out to be a discretization of a diffusion operator with homogenized coefficients obtained by solving discrete cell problems. This two-grid method is then embedded inside a multi-grid cycle extending over both the fine and the coarse scale. Received August 10, 1999; revised July 28, 2000     

An Iterative Substructuring Method for div-stable Finite Element Approximations of the Oseen Problem

We apply an iterative substructuring algorithm with transmission conditions of Robin–Robin type to the discretized Oseen problem appearing as a linearized variant of the incompressible Navier–Stokes equations. Here we consider finite element approximations using velocity/pressure pairs which satisfy the Babuška–Brezzi stability condition. After proving well-posedness and strong convergence of the method, we derive an a-posteriori error estimate which controls convergence of the discrete subdomain solutions to the global discrete solution by measuring the jumps of the velocities at the interface. Additionally we obtain information how to design a parameter of the Robin interface condition which essentially influences the convergence speed. Numerical experiments confirm the theoretical results and the applicability of the method. Received February 18, 2000; revised February 21, 2001