### Citations

3891 | A method for obtaining digital signatures and public-key cryptosystems,”
- Rivest, Shamir, et al.
- 1978
(Show Context)
Citation Context ...ions of greatest interest, this requires that information encryption and decryption is performed in real-time on mobile terminals. The de facto cryptography algorithms are Rivest-Shamir-Adleman (RSA) =-=[38]-=- and Elliptic Curve Cryptography (ECC) [32, 34]. The key operations employed by these algorithms are not directly supported by typical integer-oriented architectures used in embedded systems, like ARM... |

3539 | New directions in cryptography
- Diffie, Hellman
- 1976
(Show Context)
Citation Context ...d correspondent will be able to decrypt any messages encrypted using that key. The second class is called public-key cryptosystem and was first publicly suggested by Diffie and Hellman in their paper =-=[13]-=-. It includes as representative members RSA [38] and ECC [32, 34]. In the public-key systems both correspondents have a key pair, not just a single key. Every pair consists of a public key and a priva... |

1010 |
Elliptic curve cryptosystems
- Koblitz
- 1987
(Show Context)
Citation Context ...at information encryption and decryption is performed in real-time on mobile terminals. The de facto cryptography algorithms are Rivest-Shamir-Adleman (RSA) [38] and Elliptic Curve Cryptography (ECC) =-=[32, 34]-=-. The key operations employed by these algorithms are not directly supported by typical integer-oriented architectures used in embedded systems, like ARM [41], MicroBlaze [48], MIPS [?], and NIOS [2].... |

740 |
Use of Elliptic Curves in Cryptography
- Miller
- 1986
(Show Context)
Citation Context ...at information encryption and decryption is performed in real-time on mobile terminals. The de facto cryptography algorithms are Rivest-Shamir-Adleman (RSA) [38] and Elliptic Curve Cryptography (ECC) =-=[32, 34]-=-. The key operations employed by these algorithms are not directly supported by typical integer-oriented architectures used in embedded systems, like ARM [41], MicroBlaze [48], MIPS [?], and NIOS [2].... |

610 | Guide to Elliptic Curve Cryptography.
- Hankerson, Menezes, et al.
- 2004
(Show Context)
Citation Context ... public-key cryptosystem serves more services than the secret-key cryptosystem, but also it resolves the main issues in the secret-key cryptosystem, which are the key distribution, and key management =-=[20]-=-. However, the computational 8requirements of the private-key cryptography are much lower than those of the public-key cryptography. Therefore, both cryptosystems are often found to facilitate in conj... |

561 |
Modular multiplication without trial division,”Math.
- Montgomery
- 1985
(Show Context)
Citation Context ... Description NIST recommended curves (fast reduction) [17] Is the fastest reduction method. Only for Mersenne primes and polynomials Barrett reduction [20] Only for prime field. Montgomery Multiplier =-=[33]-=- Does the modular multiplication. Dual field support - prime and binary fields. Shift-and-add Multiplier [20] Performs only regular multiplication → need to be combined with reduction algorithm to com... |

333 |
Computer Arithmetic Algorithms and Hardware Designs,
- Parhami
- 2000
(Show Context)
Citation Context ...n(0), all carries are calculated in parallel. Finally, all the sum bits, s(i) are calculated according to Equation 5.6. It is well-known that CLA has a latency of O(log(n)), where n is the wordlength =-=[36]-=-. (maybe include carry-lookahead hierarchy diagram here). From the point of view of a reconfigurable array, CLA has an advantage against CSkA. Specifically, generate and propagate networks of Xilinx a... |

214 |
Ofman,“Multiplication of multidigit numbers on automata,”
- Karatsuba, Y
- 1963
(Show Context)
Citation Context ...ime and binary fields. Shift-and-add Multiplier [20] Performs only regular multiplication → need to be combined with reduction algorithm to complete modular multiplication. Karatsuba-Ofman Multiplier =-=[24]-=- Performs only regular multiplication → need to be combined with reduction algorithm to complete modular multiplication. Moreover, if the prime that is used in EC point multiplication is one of the NI... |

184 | Efficient elliptic curve exponentiation using mixed coordinates
- Cohen, Miyaji, et al.
- 1998
(Show Context)
Citation Context ...multiplication is operated yields different implementation of EC point addition and doubling. The coordianate that we decided to use is the modified Jacobian (Jm) coordinates proposed by Cohen et al. =-=[9]-=-. This is because that this coordinates yields the fastest EC point doubling, meaning 39 the least number of modular multiplicaton required. EC point addition and doubling in the (Jm) coordinate can b... |

157 |
Introduction to Cryptography with Coding Theory,
- Trappe, Washington
- 2006
(Show Context)
Citation Context ...nsumption in slice for CLA and RCA . . . . . . . . . . . . . . . . . . 74 6.4 Critical path in ns and area consumption in slice for comparator unit. . . . . . 75 xList of Algorithms 2.1 RSA Algorithm =-=[46]-=- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2 Modular exponentiation by square-and-multiply . . . . . . . . . . . . . . . . 11 2.3 Double-and Add Algorithm for EC Point Multipl... |

134 | The Roles of FPGAs in Reprogrammable Systems,”
- Hauck
- 1998
(Show Context)
Citation Context ... requirements, these fixedfunction devices are prone to rapid obsolence. On the other hand, the Reconfigurable Computing (RC) paradigm provides hardwarelike performance with software-like flexibility =-=[5, 21]-=-. In RC, application-specific computing units are defined and then instantiated onto a reconfigurable array. This way, a large number of customized computing units are emulated. The commercial Field-P... |

132 | Reconfigurable architectures for General-Purpose Computing,
- DeHon
- 1996
(Show Context)
Citation Context ...ormance at the expense of heterogenous logic function implementation performance. Second, FPGA active logic uses 1%, configuration memory uses 9%, and interconnection network uses 90% of the die area =-=[10]-=-, [11], [12]. Thus, we propose to increase the FPGA granularity such that a LUT drives two dedicated MUXes, as shown in Figure 5.9(a) and in Figure 5.9(b) for carry-lookahead adders and fast tree-base... |

90 |
The Density Advantage of Configurable Computing,
- DeHon
- 2000
(Show Context)
Citation Context ...he expense of heterogenous logic function implementation performance. Second, FPGA active logic uses 1%, configuration memory uses 9%, and interconnection network uses 90% of the die area [10], [11], =-=[12]-=-. Thus, we propose to increase the FPGA granularity such that a LUT drives two dedicated MUXes, as shown in Figure 5.9(a) and in Figure 5.9(b) for carry-lookahead adders and fast tree-based comparator... |

85 |
Implementing Elliptic Curve Cryptography.
- Rosing
- 1999
(Show Context)
Citation Context ...rocessor, especially for applications in wireless, handheld devices, and smart cards with small memory capacity and strict latency constraints. Cryptography applications are computationally intensive =-=[39,44]-=-. Thus, software-based implementations are inherently slow. For this reason, cryptography applications have been traditionally implemented in Application-Specific Integrated Circuits (ASIC) [40], or i... |

70 | Balancing interconnect and computation in a reconfigurable computing array (or, why you don’t really want 100% LUT utilization
- DeHon
- 1999
(Show Context)
Citation Context ...e at the expense of heterogenous logic function implementation performance. Second, FPGA active logic uses 1%, configuration memory uses 9%, and interconnection network uses 90% of the die area [10], =-=[11]-=-, [12]. Thus, we propose to increase the FPGA granularity such that a LUT drives two dedicated MUXes, as shown in Figure 5.9(a) and in Figure 5.9(b) for carry-lookahead adders and fast tree-based comp... |

58 |
Cryptography Theory and Practice, Third Edition
- Stinson
- 2006
(Show Context)
Citation Context ...rocessor, especially for applications in wireless, handheld devices, and smart cards with small memory capacity and strict latency constraints. Cryptography applications are computationally intensive =-=[39,44]-=-. Thus, software-based implementations are inherently slow. For this reason, cryptography applications have been traditionally implemented in Application-Specific Integrated Circuits (ASIC) [40], or i... |

37 | How secure are elliptic curves over composite extension fields?
- Smart
- 2001
(Show Context)
Citation Context ...ther public-key cryptosystems. Furthermore, not every elliptic curve offers strong security properties—for some curves, the Elliptic Curve Discrete Logarithm Problem (ECDLP) may be solved efficiently =-=[43]-=-; therefore, poor choice of the curve can compromise security. This is why National Institute of Standards and Technology (NIST) and Standards for Efficient Cryptography Group (SECG) have published a ... |

36 | An FPGA implementation of an elliptic curve processor over
- Mentens, rs, et al.
- 2004
(Show Context)
Citation Context ...he workload in the processor, there are two main methodologies of implementing the hardware co-processor in the literature. One is Finite State Machine (FSM), which can be found in [3], [6], [37] and =-=[35]-=-. Another is through definition of its own intstruction set, which can be found in [15], [18]. There are also papers that authors proposed hardware unit for computing only modular multiplicaton [14], ... |

35 | Seeking Solutions in Configurable Computing
- Mangione-Smith, Hutchings, et al.
- 1997
(Show Context)
Citation Context ...s the FPGA, which provides medium flexibility and performance when compared to the early-mentioned types of computing machines. FPGA is often used in conjunction with GPP to provide socalled RC [27], =-=[28]-=- an emerging computing paradigm for more than twenty years. Such a hybrid is referred to as a FCCM [5]. It works by defining custom computing resources on a per-application basis, and dynamically conf... |

32 | Efficient Permutation Instructions for Fast Software Cryptography,"
- Lee, Shi
- 2001
(Show Context)
Citation Context ...ryptography applications have been traditionally implemented in Application-Specific Integrated Circuits (ASIC) [40], or in hardwired-assists in Application-Specific Instruction set Processors (ASIP) =-=[26]-=-. Other solutions rely on coprocessors to accelerate long-integer arithmetic operations. Due to the ASIC and ASIP’s hardwired-assist lack of flexibility, a different full-custom circuit is needed for ... |

29 | High-performance carry chains for FPGAs,
- Hauck, Hosler, et al.
- 2000
(Show Context)
Citation Context ...the impact of deploying 23 dedicated resources for a truly parallele carry-lookahead network as well as a complex carry-select network that comprises a dedicated carry-select multiplexor for each bit =-=[22]-=-. As mentioned, the carry-lookahead network suffers from increasing circuit complexity and fan-out toward high-order bits. This leads to a triangular layout. The carry-select network exhibits the same... |

27 | Speeding up secure web transactions using elliptic curve cryptography - Gupta, Stebila, et al. - 2004 |

25 |
Fast montgomery modular multiplication and rsa cryptographic processor architectures,”
- McIvor, McLoone, et al.
- 2003
(Show Context)
Citation Context ...e to offload the workload in the processor, there are two main methodologies of implementing the hardware co-processor in the literature. One is Finite State Machine (FSM), which can be found in [3], =-=[6]-=-, [37] and [35]. Another is through definition of its own intstruction set, which can be found in [15], [18]. There are also papers that authors proposed hardware unit for computing only modular multi... |

18 | B.L.: ‘Configurable computing: the road ahead
- MANGIONE-SMITH, HUTCHINGS
- 1997
(Show Context)
Citation Context ...here is the FPGA, which provides medium flexibility and performance when compared to the early-mentioned types of computing machines. FPGA is often used in conjunction with GPP to provide socalled RC =-=[27]-=-, [28] an emerging computing paradigm for more than twenty years. Such a hybrid is referred to as a FCCM [5]. It works by defining custom computing resources on a per-application basis, and dynamicall... |

16 |
Custom computing machines: an introduction
- Buell, Pocek
- 1995
(Show Context)
Citation Context ... requirements, these fixedfunction devices are prone to rapid obsolence. On the other hand, the Reconfigurable Computing (RC) paradigm provides hardwarelike performance with software-like flexibility =-=[5, 21]-=-. In RC, application-specific computing units are defined and then instantiated onto a reconfigurable array. This way, a large number of customized computing units are emulated. The commercial Field-P... |

13 | A public-key cryptographic processor for RSA and ECC
- Eberle, Gura, et al.
- 2004
(Show Context)
Citation Context ...ware co-processor in the literature. One is Finite State Machine (FSM), which can be found in [3], [6], [37] and [35]. Another is through definition of its own intstruction set, which can be found in =-=[15]-=-, [18]. There are also papers that authors proposed hardware unit for computing only modular multiplicaton [14], [4], and [29]. In all cases, the modular multiplier hardware unit is implemented using ... |

5 |
Fpga montgomery modular multiplication architectures suitable for eccs over gf(p
- McIvor, McLoone, et al.
- 2004
(Show Context)
Citation Context ... is through definition of its own intstruction set, which can be found in [15], [18]. There are also papers that authors proposed hardware unit for computing only modular multiplicaton [14], [4], and =-=[29]-=-. In all cases, the modular multiplier hardware unit is implemented using the Montgomery Modular Multiplier unit (MMM unit), which can be implemented differently based on the criteria, such as the fle... |

3 |
Anantha Chandrakasan. An energy efficient reconfigurable public-key cryptograhpy processor architecture
- Goodman
- 2000
(Show Context)
Citation Context ...o-processor in the literature. One is Finite State Machine (FSM), which can be found in [3], [6], [37] and [35]. Another is through definition of its own intstruction set, which can be found in [15], =-=[18]-=-. There are also papers that authors proposed hardware unit for computing only modular multiplicaton [14], [4], and [29]. In all cases, the modular multiplier hardware unit is implemented using the Mo... |

3 |
FPGA and ASIC implementation of ECC processor for security on medical embedded system
- Park, Hwang, et al.
- 2005
(Show Context)
Citation Context ...offload the workload in the processor, there are two main methodologies of implementing the hardware co-processor in the literature. One is Finite State Machine (FSM), which can be found in [3], [6], =-=[37]-=- and [35]. Another is through definition of its own intstruction set, which can be found in [15], [18]. There are also papers that authors proposed hardware unit for computing only modular multiplicat... |

2 | Geeke Bruin-Muurling & Siddika Berna Ors Flexible hardware design for RSA and elliptic curve cryptosystems, T.Okamoto(Ed):CT-RSA - Batina - 2004 |

2 |
Novel multiplier architectures for gf(p) and gf(2n
- Savag, Tenca, et al.
- 2004
(Show Context)
Citation Context ...d [35]. Another is through definition of its own intstruction set, which can be found in [15], [18]. There are also papers that authors proposed hardware unit for computing only modular multiplicaton =-=[14]-=-, [4], and [29]. In all cases, the modular multiplier hardware unit is implemented using the Montgomery Modular Multiplier unit (MMM unit), which can be implemented differently based on the criteria, ... |

1 |
Online Elliptic Curve Cryptography Tutorial
- Inc
(Show Context)
Citation Context ...tion 2.3 can be used to form a group. An elliptic curve group over real 14 numbers consists of the points on the corresponding elliptic curve, together with a special point O called point at infinity =-=[8]-=-. Figure 2.1 is used to illustrate how the EC point addition equations are derived geometrically. A line which is drawn through two distance points, P and Q are added will intersect the third point, c... |

1 |
and Tolga Acar. Montgomery multiplication in GF(2K). Des
- Koc
- 1998
(Show Context)
Citation Context ...hifts to perform the reduction. In addition, MMM was also verified that can it not only be used in the prime field, it can also be used in the binary field if the inputs are in the form of polynomial =-=[25]-=-. In addition, it has been shown that MMM is the bottleneck for software solution. Therefore, we will only consider the MMM Algorithm for the modular multiplication implementation in reconfigurable ha... |

1 |
Alternatives in designing level-restoring buffers for interconnection networks in field-programmable gate arrays
- MILLER, SIMA, et al.
- 2007
(Show Context)
Citation Context ...nterconnect EQ(1) GT(1) GT(0) EQ(0) "1" "0" "1" GTf(0) GTf(1) EQf(0) EQf(1) "0" 0 1 0 10 1 0 1 Figure 5.12: Comparator unit using Horizontal dedicated path demostration. scribed in our previous paper =-=[31]-=- to improve the switching characteristics, we determined that the later approach shown in Figure 4-(b) is 40% faster. Therefore, extending the carry MUX is not considered any longer. LUT Level−Restori... |

1 |
A high-speed small rsa encryption lsi with low power dissipation
- Satoh, Kobayashi, et al.
- 1998
(Show Context)
Citation Context ...ve [39,44]. Thus, software-based implementations are inherently slow. For this reason, cryptography applications have been traditionally implemented in Application-Specific Integrated Circuits (ASIC) =-=[40]-=-, or in hardwired-assists in Application-Specific Instruction set Processors (ASIP) [26]. Other solutions rely on coprocessors to accelerate long-integer arithmetic operations. Due to the ASIC and ASI... |

1 |
Connecting Customized IP to the MicroBlaze Soft Processor Using the Fast Simplex Link (FSL
- Corp, Joes, et al.
- 2004
(Show Context)
Citation Context ...t Interface In order to merge the accelerated Montgomery Modular Multiplication hardware unit to our C-level software program, the Xilinx Fast Simplex Link (FSL) is used for the coprocessor interface =-=[47]-=-. FSL is a very fast dedicated connection that Xilinx provides for data transfering between MicroBlaze and the user-defined hardware unit because it brings data in and out directly from the MicroBlaze... |

1 |
Platform Studio User Guide
- Corp, Joes, et al.
- 2005
(Show Context)
Citation Context ..., only in which the profiling is supported. Then it is ported to run on the MicroBlaze embedded system after the hardware platform is configured using the Xilinx Platform Studio (XPS) SDK version 9.1 =-=[49]-=-. The output of the program is then viewed on the HyerTerminal. The accelerated hardware unit is first coded by VHDL in the Xilinx ISE (Project Navigator) v9.1.03i [53]. Each module of the hardware un... |

1 |
Curriculum Vitae Chi-Chun (Ambrose) Chu was borne
- com
- 1981
(Show Context)
Citation Context ...omputing units are defined and then instantiated onto a reconfigurable array. This way, a large number of customized computing units are emulated. The commercial Field-Programmable Gate Arrays (FPGA) =-=[2, 53]-=- are general-purposed reconfigurable devices. As such, they exhibit a large silicon area and power consumption overheads to support a broad range of applications. To reduce this overhead, we propose a... |