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High-speed Multiplier Design Using Multi-Operand MultipliersNezhad, Mohammad Reza Reshadi, Navi, Kaivan 01 April 2012 (has links)
Multipliers are used in most arithmetic computing
systems such as 3D graphics, signal processing, and etc. It
is inherently a slow operation as a large number of partial
products are added to produce the result. There has been
much work done on designing multipliers [1]-[6]. In first
stage, Multiplication is implemented by accumulation of
partial products, each of which is conceptually produced
via multiplying the whole multi-digit multiplicand by a
weighted digit of multiplier. To compute partial products,
most of the approaches employ the Modified Booth
Encoding (MBE) approach [3]-[5], [7], for the first step
because of its ability to cut the number of partial products
rows in half. In next step the partial products are reduced
to a row of sums and a row of caries which is called
reduction stage. / Multiplication is one of the major bottlenecks in most digital
computing and signal processing systems, which depends on the
word size to be executed. This paper presents three deferent
designs for three-operand 4-bit multiplier for positive integer
multiplication, and compares them in regard to timing, dynamic
power, and area with classical method of multiplication
performed on today architects. The three-operand 4-bit
multipliers structure introduced, serves as a building block for
three-operand multipliers in general
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Fast prime field arithmetic using novel large integer representationAlhazmi, Bader Hammad 10 July 2019 (has links)
Large integers are used in several key areas such as RSA (Rivest-Shamir-Adleman) public-key cryptographic system and elliptic curve public-key cryptographic system. To achieve higher levels of security requires larger key size and this becomes a limiting factor in prime finite field GF(p) arithmetic using large integers because operations on large integers suffer from the long carry propagation problem. Large integer representation has direct impact on the efficiency of the calculations and the hardware and software implementations. Attempts to use different representations such as residue number systems suffer from their own problems. In this dissertation, we propose a novel and efficient attribute-based large integer representation scheme capable of efficiently representing the large integers that are commonly used in cryptography such as the five NIST primes and the Pierpont primes used in supersingular isogeny Diffie-Hellman (SIDH) used in post-quantum cryptography. Moreover, we propose algorithms for this new representation to perform arithmetic operations such as conversions from and to binary representation, two’s complement, left-shift, numbers comparison, addition/subtraction, modular addition/subtraction, modular reduction, multiplication, and modular multiplication. Extensive numerical simulations and software implementations are done to verify the performance of the new number representation. Results show that the attribute-based large integer arithmetic operations are done faster in our proposed representation when compared with binary and residue number representations. This makes the proposed representation suitable for cryptographic applications on embedded systems and IoT devices with limited resources for better security level. / Graduate / 2020-07-04
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