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Unformatted text preview: 2 i mod 19 . I = 3 1 mod 19 = 3 I 1 = 3 2 mod 19 = I · I mod 19 = 9 I 2 = 3 4 mod 19 = I 1 · I 1 mod 19 = 5 I 3 = 3 8 mod 19 = I 2 · I 2 mod 19 = 6 I 4 = 3 16 mod 19 = I 3 · I 3 mod 19 = 17 I 5 = 3 32 mod 19 = I 4 · I 4 mod 19 = 4 3 50 = 3 32 · 3 16 · 3 2 Evaluate 3 50 mod 19 . This can be solved by repeated squaring. Set I i = 3 2 i mod 19 . I = 3 1 mod 19 = 3 I 1 = 3 2 mod 19 = I · I mod 19 = 9 I 2 = 3 4 mod 19 = I 1 · I 1 mod 19 = 5 I 3 = 3 8 mod 19 = I 2 · I 2 mod 19 = 6 I 4 = 3 16 mod 19 = I 3 · I 3 mod 19 = 17 I 5 = 3 32 mod 19 = I 4 · I 4 mod 19 = 4 3 50 mod 19 = I 5 · I 4 · I 1 mod 19 = 4 · 17 · 9 mod 19 = 4...
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This note was uploaded on 08/25/2010 for the course COMP COMP170 taught by Professor M.j.golin during the Spring '10 term at HKUST.
 Spring '10
 M.J.Golin
 Computer Science

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