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Presenter: Bader Alhazmi
Supervisor:

Date: Tue, June 25, 2019
Time: 08:30:00 - 00:00:00
Place: EOW 230

ABSTRACT

ABSTRACT

Addition is an essential operation in all cryptographic algorithms. Higher levels of security require larger key sizes and this becomes a limiting factor in GF(p) using large integers because of the carry propagation problem. We propose a novel and efficient attribute-based large integer representation scheme suitable for large integers commonly used in cryptography such as the five NIST primes and the Pierpont primes used in supersingular isogeny Diffie-Hellman (SIDH) for post-quantum cryptography. Algorithms are proposed for this new representation to implement arithmetic operations such as two's complement, addition/subtraction, comparison, sign detection and modular reduction. Algorithms are also developed for converting binary numbers to attribute representation, and vice versa. Extensive numerical simulations were done to verify the performance of the new number representation. Results show that addition is done faster in our proposed representation when compared with !

 binary and residue number system (RNS) based additions. Attribute addition outperformed RNS addition for all values of m where 128 ≤ m ≤ 32,768$ bits for all machine word sizes $w$ where 4 ≤ w ≤ 128 bits. Attribute based addition outperforms Kogge-Stone binary adders for a wide range of m when w is small. For increasing values of w, the speed advantages is evident only for large values of m. This makes the proposed number representation suitable for implementing cryptographic applications in embedded processors for Internet of Things (IoT) and consumer electronic devices where w is small.