On the Implementation of Unified Arithmetic on Binary Huff Curves

Ghosh, Santosh; Kumar, Amit; Das, Amitabh; Verbauwhede, Ingrid

doi:10.1007/978-3-642-40349-1_20

Cited by 16 publications

(63 citation statements)

References 19 publications

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“…Another FPGA based solution over newer technologies (Virtex 6 and 7) for BHC has been presented in Ref. 13, as shown in Table 7. Their work utilizes an area of 6032 slices which is 5% lesser than our design (6342) over Virtex 7.…”

Section: Synthesis and Place And Route Resultsmentioning

confidence: 99%

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Towards an Optimized Architecture for Unified Binary Huff Curves

Jafri

Islam

Imran

et al. 2017

J CIRCUIT SYST COMP

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Applying uni¯ed formula while computing point addition and doubling provides immunity to Elliptic Curve Cryptography (ECC) against power analysis attacks (a type of side channel attack). One of the popular techniques providing this uni¯edness is the Binary Hu® Curves (BHC) which got attention in 2011. In this paper we are presenting highly optimized architectures to implement point multiplication (PM) on the standard NIST curves over GF ð2 163 Þ and GF ð2 233 Þ using BHC. To achieve a high throughput over area ratio,¯rst of all, we have used a simpli¯ed arithmetic and logic unit. Secondly, we have reduced the time to compute PM through Double and Add algorithm. This is achieved by increasing the frequency of operation through a 2-stage pipelined architecture. The increase in clock cycles caused by consequent pipeline hazards is controlled through optimal scheduling of computations involved in PM. The synthesis results show that our designs can work up to a frequency of 377 MHz on Xilinx Virtex 7 FPGA. Moreover, the overall throughput/area ratio achieved through the adopted approach is up to 20% higher while comparing with available state-of-the-art solutions. J CIRCUIT SYST COMP Downloaded from www.worldscientific.com by MONASH UNIVERSITY on 04/22/17. For personal use only. A. R. Jafri et al. 1750178-2 J CIRCUIT SYST COMP Downloaded from www.worldscientific.com by MONASH UNIVERSITY on 04/22/17. For personal use only. Towards an Optimized Architecture for Uni¯ed Binary Hu® Curves 1750178-3 J CIRCUIT SYST COMP Downloaded from www.worldscientific.com by MONASH UNIVERSITY on 04/22/17. For personal use only. A. R. Jafri et al. 1750178-4 J CIRCUIT SYST COMP Downloaded from www.worldscientific.com by MONASH UNIVERSITY on 04/22/17. For personal use only.

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Section: Synthesis and Place And Route Resultsmentioning

confidence: 99%

“…Another FPGA based approach is found in Ref. 13, where uni¯ed PA law has been implemented by adopting projective coordinates to make BHC more secure against SPA.…”

Section: Introductionmentioning

confidence: 99%

Towards an Optimized Architecture for Unified Binary Huff Curves

Jafri

Islam

Imran

et al. 2017

J CIRCUIT SYST COMP

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“…In addition, to provide perfect security against our attack methods, we reconfigured the operations of the unified point addition formula. The proposed unified point addition method for the binary Huff curve using the equivalence class is just about 2∼4.4% slower than the existing unified point addition method from [8,9]. In addition, the proposed method is about 8.5∼17.5% faster than an existing countermeasure that provides same security, i.e., unified point addition using blinding operands of a field multiplication [10].…”

Section: Introductionmentioning

confidence: 93%

“…where α = (a + b)/b and β = (a + b)/a. The unified point addition formula in Equation (2) can be evaluated as described in [9]:…”

Section: Binary Huff Curve and Unified Point Additionmentioning

confidence: 99%

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Side-Channel Vulnerabilities of Unified Point Addition on Binary Huff Curve and Its Countermeasure

2018

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Unified point addition for computing elliptic curve point addition and doubling is considered to be resistant to simple power analysis. Recently, new side-channel attacks, such as recovery of secret exponent by triangular trace analysis and horizontal collision correlation analysis, have been successfully applied to elliptic curve methods to investigate their resistance to side-channel attacks. These attacks turn out to be very powerful since they only require leakage of a single power consumption trace. In this paper, using these side-channel attack analyses, we introduce two vulnerabilities of unified point addition on the binary Huff curve. Also, we propose a new unified point addition method for the binary Huff curve. Furthermore, to secure against these vulnerabilities, we apply an equivalence class to the side-channel atomic algorithm using the proposed unified point addition method.

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