Canonical%20EBS

1
Canonical EBS

• EBS_any
• Takes n number of users
• Finds a reasonable k and m such that
• n lt (km) choose (m)
• EBS_fixed
• Takes n users and k keys
• Finds a reasonable m such that
• n lt (km) choose (m)

2
Specifics

• The maximum number of combinations for any k and
  m pair are found when k and m are close.
• EBS_any works by starting k at 2, and m at 1,
  then incrementing and calculating total
  combinations using (km)CHOOSE(m)
• This maximizes n and minimized k and m

3
Specifics

• The canonical function is recursive and iterative
• A queue of all the bits is passed in along with
  a count m
• A bit is chosen, removed from the queue and
  placed on the stack
• canonical is called again with m-1
• Base case When m0 the stack is printed and
  the function returns

4
Efficiency

• The efficiency of this code should be
  O((km)CHOOSE(m) m) because it uses roughly m
  operations to generate each combination, and
  there are (km)CHOOSE(m) combinations
• (N)CHOOSE(M) grows faster than N2 M2 for a
  sufficiently large N and M
• This means that the n (user count) is greater for
  fewer keys and messages than the binary tree
  method

5
Simulation
Main(5, 3)
S
Q
5
4
3
2
1
Canonical(S, Q, 2)
S
5
4
3
2
1
Temp Q
1
Print(S)
Canonical(S, Q, 2)
S
S
2
3
2
3
1
5
4
3
2
Temp Q
1
2
3