Efficient Implementation of NIST-Compliant Elliptic Curve Cryptography for 8-bit AVR-Based Sensor Nodes

Liu, Zhe; Seo, Hwajeong; Grosschadl, Johann; Kim, Howon

doi:10.1109/tifs.2015.2491261

Cited by 53 publications

(38 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The field arithmetic operations used in ECC implementation consist of addition, subtraction, multiplication and squaring as well as inversion. Our implementation of arithmetic operations over P192 is largely based on the cryptographic library for 8-bit AVR processors described in [4]. However, in contrast to using masked Extended Euclidean Algorithm for inversion, our implementation used Fermatbased method, but have been optimized using addition chain.…”

Section: Finite Field Arithmeticmentioning

confidence: 99%

“…For field multiplication, we used Hutter-Schwabe's 2-level Karatsuba multiplication [17] for 192-bit multiplication and then do the reduction using the fast reduction algorithm in [18]. For field squaring, we access the karatsuba block squaring for multi-precision squaring [4] and perform the reduction after squaring operation. Both the multiplication and squaring are implementation in a branchless fashion.…”

Section: Finite Field Arithmeticmentioning

confidence: 99%

“…After that, a large body of research has been devoted to further speed up the ECC implementations on the AVR micro-controllers. The majority of this research enhance the implementation by advancing the performance-critical field arithmetic operation on standardized curve, e.g., Tiny-ECC [3] and implementation of NIST P-192 in [4]. Another line of research focuses on special curves or special prime fields, which exhibits nice features on 8-bit processors, such as MoTE-ECC over Optimal Prime Fields [5].…”

Section: Introductionmentioning

confidence: 99%

“…We illustrate the performance of OME curves on 8-bit micro-controller and report the record-setting execution times of regular scalar multiplication for both of fixed point and arbitrary point. Similar to the work [4], our implementation is realized in a constant-time fashion from scalar multiplication level down to field arithmetic level, which helps to thwart the physical attacks, i.e., timing attacks and simple power analysis (SCA) attacks. Our experimental results strongly prove that the OME curve is a nice candidate for high-speed implementation of ECC on embedded mocro-controllers.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Elliptic curve with Optimal mixed Montgomery-Edwards model for low-end devices

Liu

2015

Sci. China Inf. Sci.

Self Cite

View full text Add to dashboard Cite

This paper introduces a special family of twisted Edwards curve named Optimal mixed MontgomeryEdwards (OME) curves. The OME curve is proposed by exploiting the fact that every twisted Edwards curve is birationally equivalent to some elliptic curve in Montgomery form. The OME curves achieve optimal group arithmetic for both of twisted Edwards model and Montgomery model. In particular, the Montgomery model of OME curves only requires 3M + 2S and 1M + 3S + 3C to perform the point addition and point doubling operations, while 7M and 3M + 4S are needed for executing a point addition and point doubling for the twisted Edwards model of them. We also make effort to carefully choose the curve parameters and the underlying implementation field to achieve high performance. An example of OME curve is E/Fp : −x 2 +y 2 = 1−2782 2 ·x 2 y 2 over p = 2 192 − 2 64 − 1. Our implementation results on the widely used 8-bit micro-controller platforms (i.e., AVR Atmega128) further demonstrate and highlight the practical benefits of proposed OME curve on low-end device. In particular, our implementation, performed in constant-time, reduces the execution time by up to 14% and 18% for fixed point and random point scalar multiplication, respectively, when comparing with the state-of-the-art implementation on the identical platform.

show abstract

Section: Finite Field Arithmeticmentioning

confidence: 99%

Section: Finite Field Arithmeticmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Elliptic curve with Optimal mixed Montgomery-Edwards model for low-end devices

Liu

2015

Sci. China Inf. Sci.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Hence, our paper has significance, in particular, for lightweight implementations of ECC. Such implementations typically implement ECC on 8-bit or 16-bit processors (see, e.g., [10,27,37,38,43,50]) or utilize datapaths with small multipliers (e.g., 16-bit multipliers used in [47,48]). The contributions of this paper can be summarized as follows:…”

Section: Introductionmentioning

confidence: 99%

Single-Trace Side-Channel Attacks on Scalar Multiplications with Precomputations

Järvinen

Balasch

2017

Smart Card Research and Advanced Applications

View full text Add to dashboard Cite

Abstract. Single-trace side-channel attacks are a serious threat to elliptic curve cryptography in practice because they can break also cryptosystems where scalars are nonces (e.g., ECDSA). Previously it was believed that single-trace attacks can be avoided by using scalar multiplication algorithms with regular patterns of operations but recently we have learned that they can be broken with correlation tests to decide whether different operations share common operands. In this work, we extend these attacks to scalar multiplication algorithms with precomputations. We show that many algorithms are vulnerable to our attack which correlates measurements with precomputed values. We also show that successful attacks are possible even without knowledge of precomputed values by using clustering instead of correlations. We provide extensive evidence for the feasibility of the attacks with simulations and experiments with an 8-bit AVR. Finally, we discuss the effectiveness of certain countermeasures against our attacks.

show abstract

Terabit encryption in a second: Performance evaluation of block ciphers in GPU with Kepler, Maxwell, and Pascal architectures

Lee

Goi

Phan

2018

Concurrency and Computation

View full text Add to dashboard Cite

Summary With the emergence of IoT and cloud computing technologies, massive data are generated from various applications everyday and communicated through the Internet. Secure communication is essential to protect these data from malicious attacks. Block ciphers are one mechanism to offer such protection but unfortunately involve intensive computations that can be performance bottlenecks to the servers, especially when the data center needs to handle thousands of concurrent transactions. In this paper, we investigate the feasibility of the GPU as an accelerator to perform high‐speed encryption in server environments. We present optimized implementations of a conventional block cipher (AES) and new lightweight block ciphers (LEA, Chaskey, SIMON, SPECK, and SIMECK) across three new GPU architectures (Kepler, Maxwell, and Pascal). For AES, we improve the fine‐grain implementation by utilizing the warp shuffle instruction available in these three new GPU architectures, which yield a 6%‐16% improvement over the previous implementations. For LEA, Chaskey, SIMON, SPECK, and SIMECK, we first analyze why they cannot have efficient fine‐grain implementations in the GPU and then present our optimization techniques, which are able to achieve impressive encryption speeds of 1.912, 637, 1.485, 2.291, and 1.478 Tb/s, respectively, in GTX1080.

show abstract

Efficient Implementation of NIST-Compliant Elliptic Curve Cryptography for 8-bit AVR-Based Sensor Nodes

Cited by 53 publications

References 23 publications

Elliptic curve with Optimal mixed Montgomery-Edwards model for low-end devices

Elliptic curve with Optimal mixed Montgomery-Edwards model for low-end devices

Single-Trace Side-Channel Attacks on Scalar Multiplications with Precomputations

Terabit encryption in a second: Performance evaluation of block ciphers in GPU with Kepler, Maxwell, and Pascal architectures

Contact Info

Product

Resources

About