bi-directional hash chain

v0,0

?

vG,1

=

k0

v1,0

?

vG-1,1

=

k1

v2,0

?

vG-2,1

=

k2

vm,0

?

vG-m,1

=

km

vi,0

?

vG-i,1

=

ki

vn,0

?

vG-n,1

=

kn

vG-1,0

?

v1,1

=

kG-1

vG,0

?

v0,1

=

kG

…

…

…

…

…

…

…

…

v0,0 v1,0 represents v(1,0) = b(v(0,0))

v0,0 ? vG,1 = k0 represents k0 = c ( v(0,0) , v(G,1) )

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