Efficient FPGA Implementation of a Programmable Architecture for GF(p) Elliptic Curve Crypto Computations

Tawalbeh, Lo’ai; Mohammad, Abidalrahman; Gutub, Adnan

doi:10.1007/s11265-009-0376-x

Cited by 22 publications

(8 citation statements)

References 16 publications

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“…The change of the parameters 'a' and 'b' gives different elliptic curves (Certicom Corp., 2000a;2000b;Tawalbeh et al, 2010;Srivastava and Mathur, 2013). One of the crucial decisions when implementing an efficient ECC over GF(p) is deciding which point coordinates system to use.…”

Section: Elliptic Curve Cryptography Eccmentioning

confidence: 99%

“…One of the crucial decisions when implementing an efficient ECC over GF(p) is deciding which point coordinates system to use. In (Tawalbeh et al, 2010), details of three different projective coordinate systems are given. The first one is the affine coordinate where a point is represented as (X A ,Y A ).…”

Section: Elliptic Curve Cryptography Eccmentioning

confidence: 99%

“…The other coordinate systems do not use modular inversions in point addition and doubling. As mentioned in (Tawalbeh et al, 2010), the projection (X, Y) where X A = X/Z 2 and Y A = Y/Z 3 has the minimum number of modular multiplication operations.…”

Section: Elliptic Curve Cryptography Eccmentioning

confidence: 99%

“…Nasreldin et al's protocol is based on ECC which is characterized by different mathematical point operations that take huge time during its execution. Among these operations, the time complexity of ECPM is higher than any other point operations on elliptic curve (Tawalbeh et al, 2010). Therefore, by using parallel computation, the implementation of EPCM can be accelerated to improve the performance of ECC.…”

Section: The Proposed Parallel Design Of Nasreldin Et Al's Protocolmentioning

confidence: 99%

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Accelerating Digital Forensics through Parallel Computing

ElKabbany¹,

Rasslan²,

Aslan³

2018

Journal of Computer Science

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Digital crimes in the era of big data and cloud computing imposes significant challenges in digital forensics. Cloud environment provides low cost, easy management and reasonable solutions. Moreover, it supports big data structures and solutions (i.e., security, privacy and digital forensics). In order to achieve a secure digital forensics analysis in cloud environment, researchers have proposed solutions with expensive communication cost and computation overheads. Among these solutions Nasereldin et al. proposed a protocol which solves the problem of authenticity and integrity of evidence using signcryption technique. This leads to low communication and implementation overheads. Furthermore, identity-based cryptography is used to solve Public Key Infrastructure (PKI) problems. In addition, it is characterized by the ability to divide the message into small messages which is suitable for pipelining techniques. Nasreldin et al.'s signcryption protocol is based on Elliptic Curve Cryptography (ECC) which is implemented by using different mathematical operations. In this protocol, ECC mathematical operations take huge time during the execution of the algorithm. ECC consists of point doubling and point addition operations. These operations require the execution of many Montgomery modular multiplications that consume time. In this study, we introduce a technique to speed up ECC operations in order to enhance the efficiency of Nasreldin et al. protocol. In particular, we propose a multi-stage parallel design which consists of three stages. First, we speed up the point doubling and point addition operation. Secondly, we enhance the execution time of Montgomery multiplications. Finally, pipelining is used to obtain a better performance. The results show that the proposed design enhances Nasreldin et al. protocol's execution time by 47.1, 64.7, 73.5 and 79.4%, assuming that the number of nodes is 2, 4, 6 and 12, respectively.

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Section: Elliptic Curve Cryptography Eccmentioning

confidence: 99%

Section: Elliptic Curve Cryptography Eccmentioning

confidence: 99%

Section: Elliptic Curve Cryptography Eccmentioning

confidence: 99%

Section: The Proposed Parallel Design Of Nasreldin Et Al's Protocolmentioning

confidence: 99%

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Accelerating Digital Forensics through Parallel Computing

ElKabbany¹,

Rasslan²,

Aslan³

2018

Journal of Computer Science

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“…Other radix-2 MMM implementations are reported in [2], [3], [4], [5], [6], [7], [8], [9]. Amanor et al [11] have compared FPGA implementation of radix-2 MMM-based and IMM-based modular multipliers and found that the latter yields a better area-time product.…”

Section: Introductionmentioning

confidence: 99%

Pipelined modular multiplier supporting multiple standard prime fields

Alrimeih

Rakhmatov

2014

2014 IEEE 25th International Conference on Application-Specific Systems, Architectures and Processors

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Computationally-intensive cryptographic applications are critically dependent on the efficiency of modular multiplications. It is desirable for a modular multiplier to offer not only high performance, but also a certain degree of flexibility, supporting multiplications over finite fields of varying size. We propose a fast and flexible modular multiplier over five prime fields GF (p), standardized by NIST for use in elliptic curve cryptography, where the five special primes p are of size 192, 224, 256, 384, and 521 bits. A prime-specific datapath configuration of our multiplier is established automatically, based on an external control word that identifies a NIST prime in use. The pipeline latency of our multiplier (implemented on a Virtex-6 FPGA and running at 100 MHz) is 80 ns for 192-bit, 224-bit, and 256-bit NIST primes, and 200 ns for 384-bit and 521-bit NIST primes. The main limitation of this work is that our multiplier currently supports only the NIST prime fields. We believe that such a limitation is justifiable, as the NIST prime fields are widely used in practice and enable performance improvements through specialized hardware optimizations.

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