Results 11  20
of
41
Modular Multiplication and Base Extensions in Residue Number Systems
 IN 15TH IEEE SYMPOSIUM ON COMPUTER ARITHMETIC
, 2001
"... We present a new RNS modular multiplication for very large operands. The algorithm is based on Montgomery's method adapted to residue arithmetic. By choosing the moduli of the RNS system reasonably large, an eect corresponding to a redundant highradix implementation is achieved, due to the car ..."
Abstract

Cited by 11 (3 self)
 Add to MetaCart
We present a new RNS modular multiplication for very large operands. The algorithm is based on Montgomery's method adapted to residue arithmetic. By choosing the moduli of the RNS system reasonably large, an eect corresponding to a redundant highradix implementation is achieved, due to the carryfree nature of residue arithmetic. The actual computation in the multiplication takes place in constant time, where the unit of time is a few simple residue operations. However, it is necessary twice to convert values from one residue system into another, operations which take O(n) time on O(n) processors, where n is the number of moduli in the RNS systems. Thus these conversions are the bottlenecks of the method, and any future improvements in RNS base conversions, or the use of particular residue systems, can immediately be applied.
A fast algorithm for modular reduction
, 1998
"... We present an algorithm for computing the residue R = X mod M. The algorithm is based on a sign estimation technique that estimates the sign of a number represented by a carrysum pair produced by a carry save adder. Given the (n + k)bit X and the nbit M, the modular reduction algorithm computes t ..."
Abstract

Cited by 10 (0 self)
 Add to MetaCart
We present an algorithm for computing the residue R = X mod M. The algorithm is based on a sign estimation technique that estimates the sign of a number represented by a carrysum pair produced by a carry save adder. Given the (n + k)bit X and the nbit M, the modular reduction algorithm computes the nbit residue R in O(k + log n) time, and is particularly useful when the operand size is large. We also present a variant of the algorithm that performs modular multiplication by interleaving the shiftandadd and the modular reduction steps. The modular multiplication algorithm can be used to obtain efficient VLSI implementations of exponentiation cryptosystems.
Programmable Active Memories: the Coming of Age
 IEEE Trans. on VLSI
, 1994
"... Programmable Active Memories (PAM) are a novel form of universal hardware coprocessor. Based on FieldProgrammable Gate Array (FPGA) technology, a PAM is a virtual machine, controlled by a standard microprocessor, which can be dynamically configured into a large number of applicationspecific circu ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
(Show Context)
Programmable Active Memories (PAM) are a novel form of universal hardware coprocessor. Based on FieldProgrammable Gate Array (FPGA) technology, a PAM is a virtual machine, controlled by a standard microprocessor, which can be dynamically configured into a large number of applicationspecific circuits. PAMs offer a new mixture of hardware performance and software versatility. We review the important architectural features of PAMs, through the example of DECPeRLe1, an experimental device built in 1992. We analyze the virtual computing power of such coprocessors, from now into the predictable future. PAM programming is presented, in contrast to classical gatearray and full custom circuit design. Our emphasis is on large, codegenerated synchronous systems descriptions; no compromise is made with regard to the performance of the target circuits. We exhibit a dozen applications where PAM technology proves superior, both in performance and cost, to every other existing technology, inclu...
Performance of Firefly RPC
 INFORMATICA
, 1990
"... Generally speaking, publickey cryptographic systems consist of raising elements of some group such as GF(2n), Z/NZ or elliptic curves, to large powers and reducing the result modulo some given element. Such operation is often called modular exponentiation and is performed using modular multiplicati ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
Generally speaking, publickey cryptographic systems consist of raising elements of some group such as GF(2n), Z/NZ or elliptic curves, to large powers and reducing the result modulo some given element. Such operation is often called modular exponentiation and is performed using modular multiplications repeatedly. The practicality of a given cryptographic system depends heavily on how fast modular exponentiations are performed. Consequently, it also depends on how efficiently modular multiplications are done as these are at the base of the computation. This problem has received much attention over the years. Software as well as hardware efficient implementation were proposed. However, the results are scattered through the literature. In this paper we survey most known and recent methods for efficient modular multiplication, investigating and examining their strengths and weaknesses. For each method presented, we provide an adequate hardware implementation. Povzetek: Podan je pregled modernih metod kriptografije. 1
Computer security by redefining what a computer is
 in Proceedings New Security Paradigms II Workshop
, 1992
"... The security of modern networked computers is very low and must be dramatically improved. Integrity of data and programs is an essential aspect of computers. We propose approaches towards computer security in which the main trust is a cryptographically authenticated “keyboard”. The achievability fol ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
The security of modern networked computers is very low and must be dramatically improved. Integrity of data and programs is an essential aspect of computers. We propose approaches towards computer security in which the main trust is a cryptographically authenticated “keyboard”. The achievability follows from the current trend towards personal computers, workstations and notebooks. We discuss how this could increase computer security and which problems remain to be solved in such an environment. 1
Simulation Model for Hardware implementation of modular multiplication
 Proceedings of International. Conference on Simulation, WSES, Knights Island
, 2001
"... Abstract: Modular multiplication is fundamental to several publickey cryptography systems such as the RSA encryption system. It is also the most dominant part of the computation performed in such systems. The operation is time consuming for large operands. This paper examines the characteristics o ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
(Show Context)
Abstract: Modular multiplication is fundamental to several publickey cryptography systems such as the RSA encryption system. It is also the most dominant part of the computation performed in such systems. The operation is time consuming for large operands. This paper examines the characteristics of yet another architecture to implement modular multiplication. An experimental modular multiplier prototype is described in VHDL and simulated. The simulation results are presented. KeyWords: Modular multiplication, simulation, cryptosystems.
Hardware Architecture for the Montgomery Modular Multiplication
"... Abstract: Modular multiplication is the most dominant part of the computation performed in publickey cryptography systems such systems. The operation is time consuming for large operands. This paper examines the characteristics of yet another architecture to implement modular multiplication using ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Abstract: Modular multiplication is the most dominant part of the computation performed in publickey cryptography systems such systems. The operation is time consuming for large operands. This paper examines the characteristics of yet another architecture to implement modular multiplication using the fast Montgomery algorithm. An experimental Montgomery modular multiplier prototype is described and simulated. The simulation results are presented. KeyWords: modular multiplication, Montgomery algorithm, simulation, cryptosystems. 1
Hardware Architectures for Public Key Cryptography ⋆
"... This paper presents an overview of hardware implementations for the two commonly used types of Public Key Cryptography, i.e. RSA and Elliptic Curve Cryptography (ECC), both based on modular arithmetic. We first discuss the mathematical background and the algorithms to implement these cryptosystems. ..."
Abstract
 Add to MetaCart
(Show Context)
This paper presents an overview of hardware implementations for the two commonly used types of Public Key Cryptography, i.e. RSA and Elliptic Curve Cryptography (ECC), both based on modular arithmetic. We first discuss the mathematical background and the algorithms to implement these cryptosystems. Next an overview is given of the different hardware architectures which have been proposed in the literature.