Examples
As an example: v = (1,2,3,6,12,24,30,31) is an addition chain for 31 of length 7, since
- 2 = 1 + 1
- 3 = 2 + 1
- 6 = 3 + 3
- 12 = 6 + 6
- 24 = 12 + 12
- 30 = 24 + 6
- 31 = 30 + 1
Addition chains can be used for addition-chain exponentiation: so for example we only need 7 multiplications to calculate 531:
- 52 = 51 × 51
- 53 = 52 × 51
- 56 = 53 × 53
- 512 = 56 × 56
- 524 = 512 × 512
- 530 = 524 × 56
- 531 = 530 × 51
Read more about this topic: Addition Chain
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