Accelerating Scalar Conversion for Koblitz Curve Cryptoprocessors on Hardware Platforms

Roy, Sujoy Sinha; Fan, Junfeng; Verbauwhede, Ingrid

doi:10.1109/tvlsi.2014.2321282

Cited by 4 publications

(1 citation statement)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Integer encoding methods for signed-digit representation, which remove a stream of non-zero bits, include Booth encoding [1], a Fibonacci encoding [2] and Non-Adjacent Form (NAF). Compared to the other encoding methods, NAF has been used in diverse applications such as public key cryptography [3][4][5][6], packet filtering [7][8], constructing a ternary FCSRs [9][10] and analysis for medical predictive models [11]. In particular, NAF has been actively used in some exponentiation-based public-key cryptographic algorithms including RSA [12] and Elliptic Curve Cryptography (ECC) [13][14].…”

Section: Introductionmentioning

confidence: 99%

w-Bit Shifting Non-Adjacent Form Conversion

2018

KSII TIIS

View full text Add to dashboard Cite

As a unique form of signed-digit representation, non-adjacent form (NAF) minimizes Hamming weight by removing a stream of non-zero bits from the binary representation of positive integer. Thanks to this strong point, NAF has been used in various applications such as cryptography, packet filtering and so on. In this paper, to improve the NAF conversion speed of the algorithm, we propose a new NAF conversion algorithm, called-bit Shifting Non-Adjacent Form(), where is width of scanning window. By skipping some unnecessary bit comparisons, the proposed algorithm improves the NAF conversion speed of the algorithm. To verify the excellence of the algorithm, the algorithm and the algorithm are implemented in the 8-bit microprocessor ATmega128. By measuring CPU cycle counter for the NAF conversion under various input patterns, we show that the 2 algorithm not only increases the NAF conversion speed by 24% on average but also reduces deviation in the NAF conversion time for each input pattern by 36%, compared to the 2 algorithm. In addition, we show that algorithm is always faster than algorithm, regardless of the size of .

show abstract

Section: Introductionmentioning

confidence: 99%

w-Bit Shifting Non-Adjacent Form Conversion

2018

KSII TIIS

View full text Add to dashboard Cite

show abstract

Lightweight Coprocessor for Koblitz Curves: 283-Bit ECC Including Scalar Conversion with only 4300 Gates

Roy

Järvinen

Verbauwhede

2015

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

We propose a lightweight coprocessor for 16-bit microcontrollers that implements high security elliptic curve cryptography. It uses a 283-bit Koblitz curve and offers 140-bit security. Koblitz curves offer fast point multiplications if the scalars are given as specific τ-adic expansions, which results in a need for conversions between integers and τ-adic expansions. We propose the first lightweight variant of the conversion algorithm and, by using it, introduce the first lightweight implementation of Koblitz curves that includes the scalar conversion. We also include countermeasures against side-channel attacks making the coprocessor the first lightweight coprocessor for Koblitz curves that includes a set of countermeasures against timing attacks, SPA, DPA and safe-error fault attacks. When the coprocessor is synthesized for 130 nm CMOS, it has an area of only 4,323 GE. When clocked at 16 MHz, it computes one 283-bit point multiplication in 98 ms with a power consumption of 97.70 µW, thus, consuming 9.56 µJ of energy.

show abstract

Arithmetic of $$\tau $$ τ -adic expansions for lightweight Koblitz curve cryptography

2018

Self Cite

View full text Add to dashboard Cite

Koblitz curves allow very efficient elliptic curve cryptography. The reason is that one can trade expensive point doublings to cheap Frobenius endomorphisms by representing the scalar as a τ-adic expansion. Typically elliptic curve cryptosystems, such as ECDSA, also require the scalar as an integer. This results in a need for conversions between integers and the τ-adic domain, which are costly and hinder the use of Koblitz curves on very constrained devices, such as RFID tags, wireless sensors, or certain applications of the Internet-of-Things. We provide solutions to this problem by showing how complete cryptographic processes, such as ECDSA signing, can be completed in the τ-adic domain with very few resources. This allows outsourcing conversions to a more powerful party. We provide several algorithms for performing arithmetic operations in the τ-adic domain. In particular, we introduce a new representation allowing more efficient and secure computations compared to the algorithms available in the preliminary version of this work from CARDIS 2014. We also provide datapath extensions with different speed and side-channel resistance properties that require areas from less than one hundred to a few hundred gate equivalents on 0.13 µm CMOS. These extensions are applicable for all Koblitz curves.

show abstract

Accelerating Scalar Conversion for Koblitz Curve Cryptoprocessors on Hardware Platforms

Cited by 4 publications

References 26 publications

w-Bit Shifting Non-Adjacent Form Conversion

w-Bit Shifting Non-Adjacent Form Conversion

Lightweight Coprocessor for Koblitz Curves: 283-Bit ECC Including Scalar Conversion with only 4300 Gates

Arithmetic of $$\tau $$ τ -adic expansions for lightweight Koblitz curve cryptography

Contact Info

Product

Resources

About