• home
• current students
• graduate
• events

Presenter: Bader Alhazmi
Supervisor:

Date: Wed, June 26, 2019
Time: 08:30:00 - 16:00:00
Place: EOW 230

ABSTRACT

ABSTRACT

Modular multiplication is an underlying essential operation in almost all cryptographic algorithms and many other applications. To achieve higher levels of security requires larger key size 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 capable of efficiently representing the large integers 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. Algorithms are proposed for this new representation to implement integer arithmetic operations in an efficient way. We propose a fast large integer modular multiplication algorithm along with other operations required to perform the multiplication operation such as two's complement, addition/subtraction, comparison, modular reduction and left-shift operations. Algorithms are also!

  developed for converting a binary number to attribute representation, and vice versa. 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 modular multiplication operation is done faster in our proposed representation when compared with binary interleaved modular multiplication algorithm based Kogge-Stone parallel prefix adder (KSA). Attribute-based modular multiplication outperformed binary based interleaved modular multiplication for all values of integer size m where 128 ≤ m ≤ 32,768$ bits for all machine word sizes w where 4 ≤ w ≤ 128 bits. This makes the proposed representation suitable for cryptographic applications on embedded systems and Internet of Things (IoT) devices with limited resources for better security level.