• Journal of IKEEE
• /
• v.23 no.4
• /
• pp.1321-1327
• /
• 2019

This paper describes an efficient hardware implementation of modular square root (MSQR) computation over GF(p), which is the operation needed to map plaintext messages to points on elliptic curves for elliptic curve (EC)-ElGamal public-key encryption. Our method supports five sizes of elliptic curves over GF(p) defined by the National Institute of Standards and Technology (NIST) standard. For the Koblitz curves and the pseudorandom curves with 192-bit, 256-bit, 384-bit and 521-bit, the Euler's Criterion based on the characteristic of the modulo values was applied. For the elliptic curves with 224-bit, the Tonelli-Shanks algorithm was simplified and applied to compute MSQR. The proposed method was implemented using the finite field arithmetic circuit with 32-bit datapath and memory block of elliptic curve cryptography (ECC) processor, and its hardware operation was verified by implementing it on the Virtex-5 field programmable gate array (FPGA) device. When the implemented circuit operates with a 50 MHz clock, the computation of MSQR takes about 18 ms for 224-bit pseudorandom curves and about 4 ms for 256-bit Koblitz curves.

• ETRI Journal
• /
• v.40 no.3
• /
• pp.396-409
• /
• 2018

Elliptic curve cryptography (ECC) can achieve relatively good security with a smaller key length, making it suitable for Internet of Things (IoT) devices. DNA-based encryption has also been proven to have good security. To develop a more secure and stable cryptography technique, we propose a new hybrid DNA-encoded ECC scheme that provides multilevel security. The DNA sequence is selected, and using a sorting algorithm, a unique set of nucleotide groups is assigned. These are directly converted to binary sequence and then encrypted using the ECC; thus giving double-fold security. Using several examples, this paper shows how this complete method can be realized on IoT devices. To verify the performance, we implement the complete system on the embedded platform of a Raspberry Pi 3 board, and utilize an active sensor data input to calculate the time and energy required for different data vector sizes. Connectivity and resilience analysis prove that DNA-mapped ECC can provide better security compared to ECC alone. The proposed method shows good potential for upcoming IoT technologies that require a smaller but effective security system.