PEC - An Alternate and More Efficient Public Key Cryptosystem

Rahul Krishnan 

Mass Academy of Math and Science 85 Prescott Street, Worcester, MA 99999, USA

 ABSTRACT

 In an increasingly connected world, security is a top concern for Internet of Things (IoT). These IoT devices have to be inexpensive implying that they will be constrained in storage and computing resources. In order to secure such devices, highly efficient public key cryptosystems (PKC) are critical. Elliptic Curve Cryptography (ECC) is the most commonly implemented PKC in use today. In this paper, an alternate and a more efficient PKC, called the PEC (Pells Equation Cryptography) has been proposed based on Pells equation: x 2 − D ∗ y 2 ≡ 1 (mod p). It is shown that scalar multiplication in PEC is significantly more efficient compared to ECC. It is also shown that the Discrete Logarithm Problem - computing the private key from the public key - in PEC is at least as hard as that of ECC. 

KEYWORDS

Public Key Cryptography, Elliptic Curve Cryptography, Scalar Multiplication, Pell’s equation, Internet of Things

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