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

Abstract

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.

FFT enabled ECC for WSN nodes without hardware multiplier support

“…In a recent work, ECC is implemented using a different DFT based approach to realize GF (p m ) multiplications and squarings [39]. In [39], the FFT [30,35,36] is used to transform GF (p m ) elements into the frequency domain.…”

“…In a recent work, ECC is implemented using a different DFT based approach to realize GF (p m ) multiplications and squarings [39]. In [39], the FFT [30,35,36] is used to transform GF (p m ) elements into the frequency domain. Once the frequency domain representations for GF (p m ) elements are obtained, their polynomial multiplication is computed simply by pairwise multiplying their frequency domain coefficients.…”

“…With this work, similar to [39], we use FFT based multiplication to implement ECC. However, unlike in [39],…”

Improved Performance of SRAM-Based True Random Number Generator by Leveraging Irradiation Exposure

“…To keep the communication between Internet of Things (IOT) devices secure, the data often require encryption before being transmitted [1], and true random number generators (TRNGs) are indispensable primary components in many encryption algorithms [2,3]. TRNGs usually extract random numbers from the outcome of non-deterministic physical processes, such as thermal noise of resistors [4], random jitter of clock signals [5], random telegraph noise (RTN) [6] and metastable oscillation of latch circuits [7].…”

“…In experimental evaluations, the min-entropy is usually regarded as the worst-case (i.e., the greatest lower bound) measure of randomness (entropy) for SRAM power-on values [20]. The min-entropy of every bit (bit i ) in the SRAM power-on sequence can be calculated by Equations (1) and (2). H…”