In AEGIS, system integrity is preserved through the chain of integrity checks in the boostrap process. The ideal authentication chain produced by each level verifying the next can be represented by the recurrence
is a boolean value representing the integrity of level i, and
is the boolean and operation. 
is the
verification function associated with the 
level. 
takes
as its only argument the level to verify, and it returns a boolean
value as a result. The verification function performs a cryptographic
hash of the level, and compares the result to the value obtained from
a stored signature for the level. As stated earlier, the IBM PC does
not lend itself to such a boot process. Instead, we alter the
recurrence to:
Here, n represents the number of expansion boards in the system, and our level of assurance is preserved.
