Elliptic Curve Cryptography on Constrained Microcontrollers Using Frequency Domain Arithmetic

Gulen, Utku; Baktır, Selçuk

doi:10.1007/978-3-319-09153-2_37

Cited by 5 publications

(29 citation statements)

References 35 publications

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“…Gouvêa et al's work, which uses the 160-bit curve secp160r1 that has a slightly smaller elliptic curve group order than ours, achieves ECC random point multiplication in 0.58 s [68]. Our previous ECC implementation over GF((2 13 − 1) 13 ) on the MSP430F149, a similar microcontroller to the MSP430F1611, achieves random point multiplication in 1.55 s [20]. Please note that our ECC random point multiplication implementation in this work, which exploits the NTT-based finite field multiplication/squaring and the FFT, is more than 18% faster than our previous implementation on the same elliptic curve.…”

Section: Implementation Resultsmentioning

confidence: 68%

“…Public key cryptography (PKC) [19] provides a solution to the key distribution problem, yet it is considered computationally expensive for constrained WSN nodes. On the other hand, previous works prove PKC to be applicable on constrained WSN nodes for solving the key distribution problem [20][21][22][23][24]. Elliptic curve cryptography (ECC) [25,26] is a popular option for PKC.…”

Section: Introductionmentioning

confidence: 99%

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Elliptic Curve Cryptography for Wireless Sensor Networks Using the Number Theoretic Transform

Gulen

Baktır

2020

Sensors

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We implement elliptic curve cryptography on the MSP430 which is a commonly used microcontroller in wireless sensor network nodes. We use the number theoretic transform to perform finite field multiplication and squaring as required in elliptic curve scalar point multiplication. We take advantage of the fast Fourier transform for the first time in the literature to speed up the number theoretic transform for an efficient realization of elliptic curve cryptography. Our implementation achieves elliptic curve scalar point multiplication in only 0.65 s and 1.31 s for multiplication of fixed and random points, respectively, and has similar or better timing performance compared to previous works in the literature.

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Section: Implementation Resultsmentioning

confidence: 68%

Section: Introductionmentioning

confidence: 99%

Elliptic Curve Cryptography for Wireless Sensor Networks Using the Number Theoretic Transform

Gulen

Baktır

2020

Sensors

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“…While symmetric key cryptography is simpler and can be implemented efficiently on WSN nodes, public key cryptography (PKC) is significantly more complex and yet still needed for the distribution of the symmetric keys [9]. Elliptic-curve cryptography (ECC) [10,11] is a commonly used public-key cryptosystem and considered a viable remedy for distributing the secret keys in WSNs [12][13][14][15][16]. The efficiency of ECC depends on the speed of the performed arithmetic.…”

Section: Introductionmentioning

confidence: 99%

FFT enabled ECC for WSN nodes without hardware multiplier support

GÜLEN,

BAKTIR

2022

Turkish Journal of Electrical Engineering and Computer Sciences

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ECC is a popular cryptographic algorithm for key distribution in wireless sensor networks where power efficiency is desirable. A power efficient implementation of ECC without using hardware multiplier support was proposed earlier for wireless sensor nodes. The proposed implementation utilized the number theoretic transform to carry operands to the frequency domain, and conducted Montgomery multiplication, in addition to other finite field operations, in that domain. With this work, we perform in the frequency domain only polynomial multiplication and use the fast Fourier transform to carry operands between the time and frequency domains. Our ECC implementation over GF ((2 13 − 1) 13 ) on the MSP430 microcontroller implements multiplications without using a hardware multiplier. It achieves scalar multiplication with fixed and random points in only 0.89 s and 1.74 s, respectively. Our implementation achieves ECC point multiplication of fixed and random points 10% and 13% faster, and consuming 12% and 15% less energy, in comparison to the existing work.

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“…Digital signatures, provided by PKC, can be used to authenticate messages exchanged between sensor nodes. Although the computational complexity of PKC is considered a drawback for WSN nodes with constrained microcontrollers, previous works show that PKC can be a viable option [26,27,28,29,30,31]. The two most popular PKC schemes are elliptic curve cryptography (ECC) and the Rivest Shamir Addleman (RSA) cryptosystem [25,32,33].…”

Section: Introductionmentioning

confidence: 99%

Implementing RSA for Wireless Sensor Nodes

Gulen

Abdelrahman

Baktır

2019

Sensors

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As wireless sensor networks (WSNs) become more widespread, potential attacks against them also increase and applying cryptography becomes inevitable to make secure WSN nodes. WSN nodes typically contain only a constrained microcontroller, such as MSP430, Atmega, etc., and running public key cryptography on these constrained devices is considered a challenge. Since WSN nodes are spread around in the field, the distribution of the shared private key, which is used in a symmetric key cryptographic algorithm for securing communications, is a problem. Thus, it is necessary to use public key cryptography to effectively solve the key distribution problem. The RSA cryptosystem, which requires at least a 1024-bit key, is the most widely used public key cryptographic algorithm. However, its large key size is considered a drawback for resource constrained microcontrollers. On the other hand, RSA allows for extremely fast digital signature generation which may make it desirable in applications where messages transmitted by sensor nodes need to be authenticated. Furthermore, for compatibility with an existing communication infrastructure, it may be desirable to adopt RSA in a WSN setting. With this work, we show that, in spite of its long key size, RSA is applicable for wireless sensor networks when optimized arithmetic, low-level coding and some acceleration algorithms are used. We pick three versions of the MSP430 microcontroller, which is used widely on wireless sensor network nodes, and implement 1024-bit RSA on them. Our implementation achieves 1024-bit RSA encryption and decryption operations on MSP430 in only 0 . 047 s and 1 . 14 s, respectively. In order to achieve these timings, we utilize several acceleration techniques, such as the subtractive Karatsuba-Ofman, Montgomery multiplication, operand scanning, Chinese remainder theorem and sliding window method. To the best of our knowledge, our timings for 1024-bit RSA encryption and decryption operations are the fastest reported timings in the literature for the MSP430 microcontroller.

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Elliptic Curve Cryptography on Constrained Microcontrollers Using Frequency Domain Arithmetic

Cited by 5 publications

References 35 publications

Elliptic Curve Cryptography for Wireless Sensor Networks Using the Number Theoretic Transform

Elliptic Curve Cryptography for Wireless Sensor Networks Using the Number Theoretic Transform

FFT enabled ECC for WSN nodes without hardware multiplier support

Implementing RSA for Wireless Sensor Nodes

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