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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 carryfr ..."
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Cited by 7 (1 self)
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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.
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 ..."
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Cited by 5 (0 self)
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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 ..."
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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 ..."
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Cited by 2 (0 self)
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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
theoremTheorem[section] exampleExample[section] proposition[theorem]Proposition corollary[theoremCorollary lemma[theorem]Lemma
"... We present some quantitative performance measurements for the computing power of Programmable Active Memories (PAM), as introduced by [BRV89]. Based on Field Programmable Gate Array (FPGA) technology, the PAM is a universal hardware coprocessor closely coupled to a standard host computer. The PAM c ..."
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We present some quantitative performance measurements for the computing power of Programmable Active Memories (PAM), as introduced by [BRV89]. Based on Field Programmable Gate Array (FPGA) technology, the PAM is a universal hardware coprocessor closely coupled to a standard host computer. The PAM can speed up many critical software applications running on the host, by executing part of the computations through a specific hardware design. The performance measurements presented are based on two PAM architectures and ten specific applications, drawn from arithmetics, algebra, geometry, physics, biology, audio and video. Each of these PAM designs proves as fast as any reported hardware or supercomputer for the corresponding application. In cases where we could bring some genuine algorithmic innovation into the design process, the PAM was measured to be an order of magnitude faster than any previously existing system (see [SBV91] and [Sku92]). 1 PAM concept Like any RAM memory module, a...
Patrice Bertin Didier Roncin Jean Vuillemin March
 Research on Integrated Systems: Proceedings of the 1993 Symposium
, 1993
"... We present some quantitative performance measurements for the computing power of Programmable Active Memories (PAM), as introduced by [BRV89]. Based on Field Programmable Gate Array (FPGA) technology, the PAM is a universal hardware coprocessor closely coupled to a standard host computer. The PAM c ..."
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We present some quantitative performance measurements for the computing power of Programmable Active Memories (PAM), as introduced by [BRV89]. Based on Field Programmable Gate Array (FPGA) technology, the PAM is a universal hardware coprocessor closely coupled to a standard host computer. The PAM can speed up many critical software applications running on the host, by executing part of the computations through a specific hardware design. The performance measurements presented are based on two PAM architectures and ten specific applications, drawn from arithmetics, algebra, geometry, physics, biology, audio and video. Each of these PAM designs proves as fast as any reported hardware or supercomputer for the corresponding application. In cases where we could bring some genuine algorithmic innovation into the design process, the PAM was measured to be an order of magnitude faster than any previously existing system (see [SBV91] and [Sku92]). R esum e Nous presentons quelques mesures qua...
Montgomery Modular Multiplication in Residue Arithmetic
, 2000
"... 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 effect corresponding to a redundant highradix implementation is achieved, due to the carry ..."
Abstract
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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 effect 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 takes 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.
unknown title
"... The literature of cryptography has a curious history. Secrecy, of course, has always played a central role, but until the First World War, important developments appeared in print in a more or less timely fashion and the field moved forward in much the same way as other specialized disciplines. As l ..."
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The literature of cryptography has a curious history. Secrecy, of course, has always played a central role, but until the First World War, important developments appeared in print in a more or less timely fashion and the field moved forward in much the same way as other specialized disciplines. As late as 1918, one of the most influential cryptanalytic papers of the twentieth century, William F. Friedman’s monograph The Index of Coincidence and Its Applications in Cryptography, appeared as a research report of the private Riverbank Laboratories [577]. And this, despite the fact that the work had been done as part of the war effort. In the same year Edward H. Hebern of Oakland, California filed the first patent for a rotor machine [710], the device destined to be a mainstay of military cryptography for nearly 50 years. After the First World War, however, things began to change. U.S. Army and Navy organizations, working entirely in secret, began to make fundamental advances in cryptography. During the thirties and forties a few basic papers did appear in the open literature and several treatises on the subject were published, but the latter were farther and farther behind the state of the art. By the end of the war the transition was complete. With one notable exception, the public literature had died. That exception was Claude Shannon’s paper “The Communication Theory of Secrecy Systems, ” which
A Survey of Available Cryptosystems
, 2002
"... Cryptographic techniques have become a standard component in many communications settings. There is now a wide variety of tools, both in hardware and software, providing encryption for data security and digital signatures for authentication. Almost everyone involved in data transfer encounters these ..."
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Cryptographic techniques have become a standard component in many communications settings. There is now a wide variety of tools, both in hardware and software, providing encryption for data security and digital signatures for authentication. Almost everyone involved in data transfer encounters these tools in the