Fast prime field arithmetic using novel large integer representation

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dc.contributor.author Alhazmi, Bader Hammad
dc.date.accessioned 2019-07-10T22:55:12Z
dc.date.copyright 2019 en_US
dc.date.issued 2019-07-10
dc.identifier.uri http://hdl.handle.net/1828/10955
dc.description.abstract 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. en_US
dc.language English eng
dc.language.iso en en_US
dc.rights Available to the World Wide Web en_US
dc.subject Large Integer Arithmetic en_US
dc.subject Number Representation en_US
dc.subject Fast Modular Multipliers en_US
dc.subject Fast Multipliers en_US
dc.subject Large Integer Modular Multiplication en_US
dc.subject Fast Large Integer Modular Addition en_US
dc.subject Fast Large Integer Addition en_US
dc.title Fast prime field arithmetic using novel large integer representation en_US
dc.type Thesis en_US
dc.contributor.supervisor Gebali, Fayez
dc.contributor.supervisor Ibrahim, Atef
dc.degree.department Department of Electrical and Computer Engineering en_US
dc.degree.level Doctor of Philosophy Ph.D. en_US
dc.description.scholarlevel Graduate en_US
dc.description.embargo 2020-07-04

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