HYBRID ANALYSIS OF TMVP FOR MODULAR POLYNOMIAL MULTIPLICATION IN CRYPTOGRAPHY

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2022-3-07

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Efe, Giray

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Polynomial multiplication on the quotient ring Z[x]/<x^n+-1> is one of the most fundamental, general-purpose operations frequently used in cryptographic algorithms. Therefore, a possible improvement over a multiplication algorithm directly affects the performance of algorithms used in a cryptographic application. Well-known multiplication algorithms such as Schoolbook, Karatsuba, and Toom-Cook are dominant choices against NTT in small and ordinary input sizes. On the other hand, how these approaches are implemented under the quotient ring of polynomials, Z[x]/<x^n+-1>, matters. Instead of applying the reduction procedure as the final stage, using Toeplitz Matrix Product (i.e., TMVP) is a clever way to realize the modular multiplication more efficiently. Furthermore, the hybrid use of these algorithms yields more efficient results than the static choice of any single algorithm. For this purpose, we derive and analyze various constructions of multiplication and share the best possible sequences under different circumstances, and show that TMVP is a decent choice instead of classical modular polynomial multiplication approaches in cryptographic applications.

Subject Keywords

Cryptography, Modular Polynomial Multiplication, Hybrid Multiplication,TMVP, 2-way Split Multiplication, 3-way Split Multiplication, Karatsuba Multiplication, Toom-Cook Multiplication, Arithmetic Complexity Analysis, Delay Complexity Analysis, Cost Metrics, Hybrid Cost Calculation, Most Efficient Hybrid Cost Results

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https://hdl.handle.net/11511/96309

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Graduate School of Applied Mathematics, Thesis

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Citation Formats

G. Efe, “HYBRID ANALYSIS OF TMVP FOR MODULAR POLYNOMIAL MULTIPLICATION IN CRYPTOGRAPHY,” M.S. - Master of Science, Middle East Technical University, 2022.