Arithmetic of $$\tau $$ τ -adic expansions for lightweight Koblitz curve cryptography
نویسندگان
چکیده
منابع مشابه
Efficient Hyperelliptic Curve Arithmetic Using Tau-adic Expansions
INTRODUCTION Security of public key cryptographic protocols is based on the apparent difficulty of a mathematical problem. Perhaps the most famous of these problems is that of factoring a composite number into primes, on which the security of the system known as RSA [1] relies. The standard cryptographic protocols like Diffie-Hellman [2] key exchange, ElGamal [3] encryption, and digital signatu...
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This paper explores two techniques on a family of hyperelliptic curves that have been proposed to accelerate computation of scalar multiplication for hyperelliptic curve cryptosystems. In elliptic curve cryptosystems, it is known that Koblitz curves admit fast scalar multiplication, namely, the τ -adic non-adjacent form (τ -NAF). It is shown that the τ -NAF has the three properties: (1) existen...
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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 light...
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Over the past 20 years, numerous papers have been written on various aspects of ECC implementation. In this paper we investigate the superiority of the Arithmetic data compression technique over the Huffman data compression technique in reducing the channel bandwidth and the transmission time. The main purpose of data compression is to reduce the memory space or transmission time, while that of...
متن کاملOn Redundant τ -adic Expansions and Non-Adjacent Digit Sets
This paper studies τ -adic expansions of scalars, which are important in the design of scalar multiplication algorithms on Koblitz Curves, and are less understood than their binary counterparts. At Crypto ’97 Solinas introduced the width-w τ -adic non-adjacent form for use with Koblitz curves. It is an expansion of integers z = P` i=0 ziτ , where τ is a quadratic integer depending on the curve,...
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ژورنال
عنوان ژورنال: Journal of Cryptographic Engineering
سال: 2018
ISSN: 2190-8508,2190-8516
DOI: 10.1007/s13389-018-0182-0