A Substitution Box (S-Box) is an integral component of modern block ciphers that provides confusion. The term "confusion" was introduced by Shannon in 1949 and it refers to the complexity of the relationship between the key and the ciphertext. Most S-Boxes are non-linear in order to promote confusion. Due to this, the S-Box is usually the most complex component of a block cipher. The Advanced Encryption Standard (AES) features an 8-bit S-Box where the output depends on the Galois field multiplicative inverse of the input.

MK-3 is a sponge based Authenticated Encryption (AE) algorithm which provides both authenticity and confidentiality. It was developed through a joint effort between the Rochester Institute of Technology and the former Harris Corporation, now L3Harris. The MK-3 algorithm has a state that is 512 bits wide and it uses 32 instances of a 16-bit S-Box to cover the entire state. These 16-bit S-Boxes are similar to what is seen in the AES, however, they are notably larger and more complex.

Binary Galois field arithmetic is well suited to hardware implementations where addition and multiplication are mapped to a combination of basic XOR and AND operations. A simple method to calculate Galois field multiplicative inversion is through the extended Euclidean algorithm. This is, however, very expensive to implement in hardware. A possible solution is to use a composite field representation, where the original operation is broken down to a series of simpler operations in the base field. This lends itself very well to implementations that consume less area and power with better performance.

Given the size and number of the S-Boxes in MK-3, these units contribute to the majority of the implementation resources. Several composite field structures are explored in this work which provide different area utilization and clock frequency characteristics. This thesis evaluates the composite field structures and recommends several candidates for high performing MK-3 Field Programmable Gate Array (FPGA) applications.

Library of Congress Subject Headings

Field programmable gate arrays--Security measures; Ciphers--Evaluation

Publication Date


Document Type


Student Type


Degree Name

Computer Engineering (MS)

Department, Program, or Center

Computer Engineering (KGCOE)


Marcin Lukowiak

Advisor/Committee Member

Stanislaw Radziszowski

Advisor/Committee Member

Sonia Lopez Alarcon


RIT – Main Campus

Plan Codes