Inherent Resistance of Efficient ECC Designs against SCA Attacks

Dyka, Zoya; Bock, Estuardo Alpírez; Kabin, Ievgen; Langendoerfer, Peter

doi:10.1109/ntms.2016.7792457

Cited by 14 publications

(9 citation statements)

References 5 publications

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“…To avoid the successful revealing of k l-2 we implemented Algorithm 2 based on publications [12,13] i.e. we implemented a modified version of Algorithm 1.…”

Section: Our Implementation Of the Montgomery Kpmentioning

confidence: 99%

“…The modification done in Algorithm 2 in comparison to the Algorithm 1 refers to the initialization phase and the processing of k l−2 . The operation flow for processing k l−2 (see lines 2-8 in Algorithm 2) differs from the operation flow in the main loop (see lines [9][10][11][12][13][14][15][16][17]. The processing of key bit k l−2 consists of 5 multiplications, 5 squarings, 3 additions and 8 write to register operations, independent of the value of k l−2 .…”

Section: Our Implementation Of the Montgomery Kpmentioning

confidence: 99%

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Resistance of the Montgomery Ladder Against Simple SCA: Theory and Practice

et al. 2021

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The Montgomery kP algorithm i.e. the Montgomery ladder is reported in literature as resistant against simple SCA due to the fact that the processing of each key bit value of the scalar k is done using the same sequence of operations. We implemented the Montgomery kP algorithm using Lopez-Dahab projective coordinates for the NIST elliptic curve B-233. We instantiated the same VHDL code for a wide range of clock frequencies for the same target FPGA and using the same compiler options. We measured electromagnetic traces of the kP executions using the same input data, i.e. scalar k and elliptic curve point P, and measurement setup. Additionally, we synthesized the same VHDL code for two IHP CMOS technologies, for a broad spectrum of frequencies. We simulated the power consumption of each synthesized design during an execution of the kP operation, always using the same scalar k and elliptic curve point P as inputs. Our experiments clearly show that the success of simple electromagnetic analysis attacks against FPGA implementations as well as the one of simple power analysis attacks against synthesized ASIC designs depends on the target frequency for which the design was implemented and at which it is executed significantly. In our experiments the scalar k was successfully revealed via simple visual inspection of the electromagnetic traces of the FPGA for frequencies from 40 to 100 MHz when standard compile options were used as well as from 50 MHz up to 240 MHz when performance optimizing compile options were used. We obtained similar results attacking the power traces simulated for the ASIC. Despite the significant differences of the here investigated technologies the designs’ resistance against the attacks performed is similar: only a few points in the traces represent strong leakage sources allowing to reveal the key at very low and very high frequencies. For the “middle” frequencies the number of points which allow to successfully reveal the key increases when increasing the frequency.

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“…To avoid the successful revealing of k l-2 we implemented Algorithm 2 based on publications [12,13] i.e. we implemented a modified version of Algorithm 1.…”

Section: Our Implementation Of the Montgomery Kpmentioning

confidence: 99%

Section: Our Implementation Of the Montgomery Kpmentioning

confidence: 99%

Resistance of the Montgomery Ladder Against Simple SCA: Theory and Practice

et al. 2021

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“…In our implementation the main loop of the algorithm consists of multiplications, squarings and additions of the GF(2 233 )-elements. The division of GF (2 233 )-elements is calculated as a sequence of field squarings and field multiplications using the little theorem of Fermat: The implemented algorithm is a modification of the Montgomery kP algorithm that is based on Algorithm 2 in [9]. This implementation allows to perform all operations in parallel to the field multiplications.…”

Section: A Structure Of the Implemented Kp Designsmentioning

confidence: 99%

“…But these countermeasures are not effective against horizontal DPA [8] attacks, i.e. against attacks analysing only one measured trace using statistical methods, for example using the difference of the mean as described in [9]. Even if each key bit is processed using exactly the same operation sequence, the data dependability can result in a successfully revealed key if horizontal DPA attacks are applied [10].…”

Section: Introductionmentioning

confidence: 99%

Horizontal DPA Attacks against ECC: Impact of Implemented Field Multiplication Formula

Kabin

Dyka

Klann

et al. 2019

2019 14th International Conference on Design &Amp; Technology of Integrated Systems in Nanoscale Era (DTIS)

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Due to the nature of applications such as critical infrastructure and the Internet of Things etc. side channel analysis attacks are becoming a serious threat. Side channel analysis attacks take advantage from the fact that the behavior of crypto implementations can be observed and provides hints that simplify revealing keys. A new type of SCA are the so called horizontal SCAs. Well known randomization based countermeasures are effective means against vertical DPA attacks but they are not effective against horizontal DPA attacks. In this paper we investigate how the formula used to implement the multiplication of GF(2 n )-elements influences the results of horizontal DPA attacks against a Montgomery kPimplementation. We implemented 5 designs with different partial multipliers, i.e. based on different multiplication formulae. We used two different technologies, i.e. a 130 and a 250 nm technology, to simulate power traces for our analysis. We show that the implemented multiplication formula influences the success of horizontal attacks significantly, but we also learned that its impact differs from technology to technology. Our analysis also reveals that the use of different multiplication formulae as the single countermeasure is not sufficient to protect cryptographic designs against horizontal DPA attacks.

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“…Our kP design is a balanced and efficient implementation of the kP algorithm based on Algorithm 2 published in [7], that is a modification of the Montgomery kP algorithm.…”

Section: Investigated Kp Designsmentioning

confidence: 99%

Methods for Increasing the Resistance of Cryptographic Designs Against Horizontal DPA Attacks

Kabin

Dyka

Kreiser

et al. 2018

Information and Communications Security

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Side channel analysis attacks, especially horizontal DPA and DEMA attacks, are significant threats for cryptographic designs. In this paper we investigate to which extend different multiplication formulae and randomization of the field multiplier increase the resistance of an ECC design against horizontal attacks. We implemented a randomized sequence of the calculation of partial products for the field multiplication in order to increase the security features of the field multiplier. Additionally, we use the partial polynomial multiplier itself as a kind of countermeasure against DPA attacks. We demonstrate that the implemented classical multiplication formula can increase the inherent resistance of the whole ECC design. We also investigate the impact of the combination of these two approaches. For the evaluation we synthesized all these designs for a 250 nm gate library technologies, and analysed the simulated power traces. All investigated protection means help to decrease the success rate of attacks significantly: the correctness of the revealed key was decreased from 99% to 69%.

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Inherent Resistance of Efficient ECC Designs against SCA Attacks

Cited by 14 publications

References 5 publications

Resistance of the Montgomery Ladder Against Simple SCA: Theory and Practice

Resistance of the Montgomery Ladder Against Simple SCA: Theory and Practice

Horizontal DPA Attacks against ECC: Impact of Implemented Field Multiplication Formula

Methods for Increasing the Resistance of Cryptographic Designs Against Horizontal DPA Attacks

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