Efficiency Improvement for NTRU

Johannes BuchmannMartin DöringRichard Lindner

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Quantum Computer Attacks

1980 1990 2000 QComputer∙∙∙

RSA ECC McEliece Merkle NTRU

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NTRU

Patented in 1996 Sony & Greylock invested $11M IEEE Standard Proposal 1363.1 (in progress)

7x faster than RSA Message Expansion Parameters often updated

Hoffstein, Pipher, Silverman

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NTRU Trapdoor

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NAEP EncryptionInput

Output

Slow

Fast

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NAEP DecryptionInput

Output

Slow

Fast

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Multiplication with Binary Polynomials

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Standard Multiplication

Calculate rotations Add

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Sliding Window Multiplication

(Pre-)Calculate for Calculate rotations Add

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Pattern Multiplication

33% of recurring patterns have Precalculation is not always possible Not all patterns are needed Finding needed patterns is easy

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Pattern Multiplication

Calculate needed Calculate rotations Add

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Comparative Timings

0

0,2

0,4

0,6

0,8

1

time

[ms] Standard

Sliding WindowPattern

Platform: Pentium M, 1.6 GHz, 2GB RAM, JRE 1.6

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Try it yourself

www.flexiprovider.de

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Trinary Case

Easy as binary case

Can reuse patterns

Thank You