Shifting Primes: Extension of Pseudo-Mersenne Primes to Optimize ECC for MSP430-Based Future Internet of Things Devices

Marín, Leandro; Jara, Antonio J.; Skarmeta, Antonio F.

doi:10.1007/978-3-642-23300-5_16

Cited by 14 publications

(19 citation statements)

References 11 publications

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“…[18]), it bears the potential for noticeable speed-ups through optimization. In essence, squaring is a special case of multiplication since all partial products of the form ai · aj with i = j appear twice in the result due to the fact that ai · aj = aj · ai.…”

Section: Multiple-precision Squaringmentioning

confidence: 99%

“…TinyECC supports elliptic curves over 128, 160, and 192-bit primes fields and is highly scalable and configurable. In the past 5 years, the majority of research focussed on improving the execution time of the arithmetic operations in the underlying prime field, in particular the multiplication; examples for this line of research are [5,9,18,20,23,27]. Only very recently, a second approach to speed up ECC on the MSP430 platform has been investigated, namely the use of "special" families of curves (e.g.…”

Section: Introductionmentioning

confidence: 99%

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Efficient Implementation of ECDH Key Exchange for MSP430-Based Wireless Sensor Networks

Liu

Seo

et al. 2015

Proceedings of the 10th ACM Symposium on Information, Computer and Communications Security

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Public-Key Cryptography (PKC) is an indispensable building block of modern security protocols, and, thus, essential for secure communication over insecure networks. Despite a significant body of research devoted to making PKC more "lightweight," it is still commonly perceived that software implementations of PKC are computationally too expensive for practical use in ultra-low power devices such as wireless sensor nodes. In the present paper we aim to challenge this perception and present a highly-optimized implementation of Elliptic Curve Cryptography (ECC) for the TI MSP430 series of 16-bit microcontrollers. Our software is inspired by MoTE-ECC and supports scalar multiplication on two families of elliptic curves, namely Montgomery and twisted Edwards curves. However, in contrast to MoTE-ECC, we use pseudo-Mersenne prime fields as underlying algebraic structure to facilitate inter-operability with existing ECC implementations. We introduce a novel "zig-zag" technique for multiple-precision squaring on the MSP430 and assess its execution time. Similar to MoTE-ECC, we employ the Montgomery model for variable-base scalar multiplications and the twisted Edwards model if the base point is fixed (e.g. to generate an ephemeral key pair). Our experiments show that the two scalar multiplications needed to perform an ephemeral ECDH key exchange can be accomplished in 4.88 million clock cycles altogether (using a 159-bit prime field), which sets a new speed record for ephemeral ECDH on a 16-bit processor. We also describe the curve generation process and analyze the execution time of various field and point arithmetic operations on curves over a 159-bit and a 191-bit pseudo-Mersenne prime field.

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Section: Multiple-precision Squaringmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Efficient Implementation of ECDH Key Exchange for MSP430-Based Wireless Sensor Networks

Liu

Seo

et al. 2015

Proceedings of the 10th ACM Symposium on Information, Computer and Communications Security

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“…Shifting primes are a family of pseudo-mersenne primes that were designed, in [4], to optimize the ECC cryptography primitives when the CPU is not supporting a hardware multiplication. This type of constrained CPUs is the commonly used in sensors and actuators for home automation and mobile health products.…”

Section: Shifting Primesmentioning

confidence: 99%

“…Similar primes to the shifting primes have been previously mentioned in [14], but they did not exploited its properties and applications. These new properties which are the used to optimize the implementation for constrained devices without hardware multiplier were described in [4]. In addition, this work presents new features for its optimization in CPUs with hardware multiplication support.…”

Section: Shifting Primesmentioning

confidence: 99%

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Shifting Primes on OpenRISC Processors with Hardware Multiplier

Marín

Jara

Skarmeta

2013

Lecture Notes in Computer Science

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Abstract. Shifting primes have proved its efficiency in CPUs without hardware multiplier such as the located at the MSP430 from Texas Instruments. This work analyzes and presents the advantages of the shifting primes for CPUs with hardware multiplier such as the JN5139 from NX-P/Jennic based on an OpenRISC architecture. This analysis is motivated because Internet of Things is presenting several solutions and use cases where the integrated sensors and actuators are sometimes enabled with higher capabilities. This work has concluded that shifting primes are offering advantages with respect to other kind of primes for both with and without hardware multiplier. Thereby, offering a suitable cryptography primitives based on Elliptic Curve Cryptography (ECC) for the different families of chips used in the Internet of Things solutions. Specifically, this presents the guidelines to optimize the implementation of ECC when it is presented a limited number of registers.

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Energy-Efficient Elliptic Curve Cryptography for MSP430-Based Wireless Sensor Nodes

Liu

Groβschädl

et al. 2016

Lecture Notes in Computer Science

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Abstract. The Internet is rapidly evolving from a network of personal computers and servers to a network of smart objects ("things") able to communicate with each other and with central resources. This evolution has created a demand for lightweight implementations of cryptographic algorithms suitable for resource-constrained devices such as RFID tags and wireless sensor nodes. In this paper we describe a highly optimized software implementation of Elliptic Curve Cryptography (ECC) for the MSP430 series of ultra-low-power 16-bit microcontrollers. Our software is scalable in the sense that it supports prime fields and elliptic curves of different order without recompilation, which allows for flexible tradeoffs between execution time (i.e. energy consumption) and security. The low-level modular arithmetic is optimized for pseudo-Mersenne primes of the form p = 2 n − c where n is a multiple of 16 minus 1 and c fits in a 16-bit register. All prime-field arithmetic functions are parameterized with respect to the length of operands (i.e. the number of 16-bit words they consist of) and written in Assembly language, whereby we avoided conditional jumps and branches that could leak information about the secret key. Our ECC implementation can perform scalar multiplication on two types of elliptic curves, namely Montgomery curves and twisted Edwards curves. A full scalar multiplication using a Montgomery curve over a 159-bit field requires about 3.86 · 10 6 clock cycles when executed on an MSP430F1611 microcontroller.

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Shifting Primes: Extension of Pseudo-Mersenne Primes to Optimize ECC for MSP430-Based Future Internet of Things Devices

Cited by 14 publications

References 11 publications

Efficient Implementation of ECDH Key Exchange for MSP430-Based Wireless Sensor Networks

Efficient Implementation of ECDH Key Exchange for MSP430-Based Wireless Sensor Networks

Shifting Primes on OpenRISC Processors with Hardware Multiplier

Energy-Efficient Elliptic Curve Cryptography for MSP430-Based Wireless Sensor Nodes

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