#### DMCA

## High Performance Elliptic Curve Cryptographic Co-processor (2003)

Citations: | 10 - 2 self |

### Citations

3313 | Handbook of Applied Cryptography
- Menezes, Oorschot, et al.
- 1997
(Show Context)
Citation Context ...tructures. They are finite groups and finite fields. This first section provides an introduction to these 5sCHAPTER 2. BACKGROUND 6 concepts. The definitions and theorems have been gathered from [9], =-=[23]-=- and [29] and are given without proof. These texts as well as [4] and [21] provide further discussion of the mathematics behind elliptic curve cryptography. 2.1.1 Groups Definition 1. Let G be a set. ... |

1003 |
Elliptic curve cryptosystems.
- Koblitz
- 1987
(Show Context)
Citation Context ... of Finite Field Units for Point Doubling . . . . . . . . . . 73 xiisChapter 1 Introduction 1.1 Motivation The use of elliptic curves in cryptographic applications was first proposed independently in =-=[17]-=- and [24]. Since then several algorithms have been developed whose strength relies on the difficulty of the discrete logarithm problem over a group of elliptic curve points. Prominent examples include... |

736 |
Use of Elliptic Curves in Cryptography
- Miller
- 1986
(Show Context)
Citation Context ...e Field Units for Point Doubling . . . . . . . . . . 73 xiisChapter 1 Introduction 1.1 Motivation The use of elliptic curves in cryptographic applications was first proposed independently in [17] and =-=[24]-=-. Since then several algorithms have been developed whose strength relies on the difficulty of the discrete logarithm problem over a group of elliptic curve points. Prominent examples include the Elli... |

328 |
Elliptic curve public key cryptosystems, The Kluwer
- Menezes
- 1993
(Show Context)
Citation Context ...ore, projective coordinates will provide us the best performance for NIST curves. Several flavors of projective coordinates have been proposed over the last few years. The prominent ones are Standard =-=[22]-=-, Jacobian [5, 14] and López & Dahab [20] projective coordinates. If the affine representation of P be denoted as (x, y) and the projective representation of P be denoted as (X, Y, Z), then the relati... |

181 | A survey of fast exponentiation methods
- Gordon
- 1998
(Show Context)
Citation Context ...re approximately l/2 point additions and l − 1point doubles. Several recoding methods have been proposed which in effect reduce the number of additions. In this section two methods are discussed; NAF =-=[11, 31]-=- and τ-adic NAF [18, 31]. 4.2.1 Scalar Multiplication using Binary NAF The symbols in the binary expansion are selected from the set {0, 1}. If this set is increased to {0, 1, −1} the expansion is ref... |

152 |
CM-curves with good cryptographic properties
- Koblitz
- 1991
(Show Context)
Citation Context ... co-processor capable of computing the scalar multiple of an elliptic curve point. While the coprocessor supports all curves over a single binary field, it is optimized for the special Koblitz curves =-=[18]-=-. To demonstrate the feasibility and efficiency of both the finite field arithmetic units and the elliptic curve cryptographic co-processor, the latter has been implemented in hardware using a field p... |

141 |
Finite Fields for Computer Scientists and Engineers
- McEliece
- 1987
(Show Context)
Citation Context ...ovides an introduction to these 5sCHAPTER 2. BACKGROUND 6 concepts. The definitions and theorems have been gathered from [9], [23] and [29] and are given without proof. These texts as well as [4] and =-=[21]-=- provide further discussion of the mathematics behind elliptic curve cryptography. 2.1.1 Groups Definition 1. Let G be a set. A binary operation on G is a function that assigns each ordered pair of el... |

127 |
Sequences of numbers generated by addition in formal groups and new primality and factorization tests
- Chudnovsky, Chudnovsky
- 1986
(Show Context)
Citation Context ... coordinates will provide us the best performance for NIST curves. Several flavors of projective coordinates have been proposed over the last few years. The prominent ones are Standard [22], Jacobian =-=[5, 14]-=- and López & Dahab [20] projective coordinates. If the affine representation of P be denoted as (x, y) and the projective representation of P be denoted as (X, Y, Z), then the relation between affine ... |

126 |
A fast algorithm for computing multiplicative inverses in gf(2m) using normal bases.
- Itoh, Tsujii
- 1988
(Show Context)
Citation Context ...Cs +3)(m − 1) + (Cm +3)(m − 2) clock cycles. For the field GF(2 163 )whereCs =1andCm = 4, this translates to 1775 clock cycles. Performance can be improved by using Algorithm 6 due to Itoh and Tsujii =-=[15]-=-. � 22m−1 �2 −1 which is This algorithm is derived from the equation a (−1) ≡ a 2m −2 ≡sCHAPTER 3. HIGH PERFORMANCE FINITE FIELD ARITHMETIC 43 true for any element a ∈GF(2 m ). From a 2t ⎧ � ⎪⎨ a −1 ≡... |

114 |
An implementation of elliptic curve cryptosystems over f2155 . In
- Agnew, Mullin, et al.
- 1993
(Show Context)
Citation Context ...egorized into three functional groups. They are 1. Accelerators which use general purpose processors to implement curve operations but implement the finite field operations using hardware. References =-=[2]-=- and [32] are examples of this. Both of these implementations support the composite field GF(2 155 ). 2. Accelerators which perform both the curve and field operations in hardware but use a small fiel... |

92 |
Contemporary Abstract Algebra,
- Gallian
- 1999
(Show Context)
Citation Context ...aic structures. They are finite groups and finite fields. This first section provides an introduction to these 5sCHAPTER 2. BACKGROUND 6 concepts. The definitions and theorems have been gathered from =-=[9]-=-, [23] and [29] and are given without proof. These texts as well as [4] and [21] provide further discussion of the mathematics behind elliptic curve cryptography. 2.1.1 Groups Definition 1. Let G be a... |

86 | A high-performance reconfigurable elliptic curve processor for gf(2m).
- Orlando, Paar
- 1965
(Show Context)
Citation Context ...CO-PROCESSOR ARCHITECTURE 48 3. Accelerators which perform both curve and field operations in hardware and use fields of cryptographic strength such as GF(2 163 ). Processors in this category include =-=[3, 12, 19, 26, 28]-=-. The work discussed in this chapter falls into category three. The architectures proposed in [26] and [28] were the first reported cryptographic strength elliptic curve co-processors. Montgomery scal... |

63 | Improved algorithms for elliptic curve arithmetic
- Lopez, Dahab
- 1999
(Show Context)
Citation Context ...us the best performance for NIST curves. Several flavors of projective coordinates have been proposed over the last few years. The prominent ones are Standard [22], Jacobian [5, 14] and López & Dahab =-=[20]-=- projective coordinates. If the affine representation of P be denoted as (x, y) and the projective representation of P be denoted as (X, Y, Z), then the relation between affine and projective coordina... |

32 | An end-to-end systems approach to elliptic curve cryptography.
- Gura, Eberle, et al.
- 2002
(Show Context)
Citation Context ...CO-PROCESSOR ARCHITECTURE 48 3. Accelerators which perform both curve and field operations in hardware and use fields of cryptographic strength such as GF(2 163 ). Processors in this category include =-=[3, 12, 19, 26, 28]-=-. The work discussed in this chapter falls into category three. The architectures proposed in [26] and [28] were the first reported cryptographic strength elliptic curve co-processors. Montgomery scal... |

22 | A Microcoded Elliptic Curve Processor Using FPGA Technology
- Leong, Leung
(Show Context)
Citation Context ...CO-PROCESSOR ARCHITECTURE 48 3. Accelerators which perform both curve and field operations in hardware and use fields of cryptographic strength such as GF(2 163 ). Processors in this category include =-=[3, 12, 19, 26, 28]-=-. The work discussed in this chapter falls into category three. The architectures proposed in [26] and [28] were the first reported cryptographic strength elliptic curve co-processors. Montgomery scal... |

21 | Elliptic curve cryptosystems on reconfigurable hardware
- Rosner
- 1998
(Show Context)
Citation Context ...site field GF(2 155 ). 2. Accelerators which perform both the curve and field operations in hardware but use a small field size such as GF(2 53 ). Architectures of this type include those proposed in =-=[30]-=- and [10]. In [30], a processor for the field GF(2 168 )is synthesized, but not implemented. Both works discuss methods to extend their implementation to a larger field size but do not actually do so.... |

19 |
Elliptic curve scalar multiplier design using FPGAs
- Gao, Shrivastava, et al.
- 1999
(Show Context)
Citation Context ...d GF(2 155 ). 2. Accelerators which perform both the curve and field operations in hardware but use a small field size such as GF(2 53 ). Architectures of this type include those proposed in [30] and =-=[10]-=-. In [30], a processor for the field GF(2 168 )is synthesized, but not implemented. Both works discuss methods to extend their implementation to a larger field size but do not actually do so. 47sCHAPT... |

18 |
Look-up table-based large finite field multiplication in memory constrained cryptosystems
- Hasan
- 2000
(Show Context)
Citation Context ...aphic co-processor has been discussed. The co-processor takes advantage of multiplication and squaring arithmetic units which are based on the look-up table-based multiplication algorithm proposed in =-=[13]-=-. Field elements are represented with respect to the polynomial basis. While the base point and resulting scalar are given in affine coordinates, internal arithmetic is performed using projective coor... |

9 |
P1363: Editorial Contribution to standard for Public Key Cryptography
- IEEE
- 2003
(Show Context)
Citation Context ...lty of the discrete logarithm problem over a group of elliptic curve points. Prominent examples include the Elliptic Curve Digital Signature Algorithm (ECDSA) [25], EC El-Gammal and EC Diffie Hellman =-=[14]-=-. In each case the underlying cryptographic primitive is elliptic curve scalar multiplication. This operation is by far the most computationally intensive step in each algorithm. In applications where... |

9 | Improved algorithms for arithmetic on anomalous binary curves",
- Solinas
- 1999
(Show Context)
Citation Context ...re approximately l/2 point additions and l − 1point doubles. Several recoding methods have been proposed which in effect reduce the number of additions. In this section two methods are discussed; NAF =-=[11, 31]-=- and τ-adic NAF [18, 31]. 4.2.1 Scalar Multiplication using Binary NAF The symbols in the binary expansion are selected from the set {0, 1}. If this set is increased to {0, 1, −1} the expansion is ref... |

7 |
An improved implementation of elliptic curves over GF (2n) when using projective point arithmetic
- King
(Show Context)
Citation Context ...esources than the bit parallel method. In [13] a digit serial multiplier is proposed which is based on look-up tables. This method was implemented in software for the field GF(2 163 ) and reported in =-=[16]-=-. To the best of our knowledge this performance of 0.540 µ-seconds for a single field multiplication is the fastest reported result for a software implementation. In this section the possibilities of ... |

2 |
Naoya Torii, Kouichi Itoh, and Masahiko Takenaka. Implementation of elliptic curve cryptographic coprocessor over GF(2 m ) on an FPGA
- Okada
- 2000
(Show Context)
Citation Context |

1 |
von zur Gathen, Jamshid Shokrollahi, and Jurgen Teich. Implementation of elliptic curve cryptographic coprocessor over GF(2 m ) on an FPGA
- Bednara, Daldrup, et al.
- 2002
(Show Context)
Citation Context |

1 |
Low Complexity and Fault Tolerant Arithmetic in Binary Extended Finite Fields
- Reyhani-Masoleh
- 2001
(Show Context)
Citation Context .... They are finite groups and finite fields. This first section provides an introduction to these 5sCHAPTER 2. BACKGROUND 6 concepts. The definitions and theorems have been gathered from [9], [23] and =-=[29]-=- and are given without proof. These texts as well as [4] and [21] provide further discussion of the mathematics behind elliptic curve cryptography. 2.1.1 Groups Definition 1. Let G be a set. A binary ... |

1 | Design and implemntation of arithmetic processor F 2 155 for elliptic curve cryptosystems - Sutikno, Eendi, et al. - 1998 |