7.8 Methods for Controlling Safety …
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functions, such as XOR. When the writing of this work began, back in 2000, the
above-mentioned ICIDs were the only uncloneable identifiers known [130]. Therefore, IC developers employed special measures to prevent the source data for the
programmable part from being copied by anyone to other chips, which protects
microcircuits from possible malicious attacks aimed at copying (redesigning) them.
The analysis results provided in [128, 129] demonstrate that it is theoretically
possible to achieve a fairly high quantity of such rearrangements with very low
financial costs. One of the disadvantages of the presented hardware metering method,
which is evident to the experts, consists in additional financial and timing costs
of introducing such programmable part of the circuit in ASIC chips, since it will
require the use of additional operations with masks, leading to additional financial
costs. Moreover, two evident variants of the results of such IC analysis are presented
in literature: (1) the first series of analyses performed answers the question: “How
many such experiments will be required to make a conclusion about the absence of
any unauthorized components in the examined microcircuit with a certain level of
reliability?”; 2) repeated series of analyses shall be aimed at assessing the specific
quantity of unauthorized copies of IC chips made by intruders if replicated chips are
actually found in the microcircuit market.
Below we are going to take a brief look at the analysis of two possible versions
of further effects.
(1) Assume that the design center of the ordered microcircuits demands the foundry
to produce no more than n copies, while the foundry actually produces N chips,
where N » n. If a foundry produces k—1 illegal copies of such chip, the total
quantity of such potential ICs will be N = k n. It should be noted that, according
to authoritative experts, a pirate foundry has a better chance of staying undetected if only an equal number of copies of each original chip are produced.
Actually, if we extract l from N objects consisting of k copies of separate designs,
the probability of absence of duplication will be expressed as follows [116]:
Prob [n, k, l] =
1 −
k − 1
N − 1
·
1 −
2(k − 1)
N − 2
· ··
1 −
(l − 1)(k − 1)
N − l − l
However, it is necessary to remember that the upper threshold of this quantity will
be determined by the following expression:
Prob [n, k, l] ≤
1 −
p
n
·
1 −
2 p
n
· · ·
1 −
(l − 1) · p
n
,
where p = 1—1/k.
For developers who failed their math exams during school studies, it is necessary to
provide certain explanations that will help the readers examine this issue more deeply
715
functions, such as XOR. When the writing of this work began, back in 2000, the
above-mentioned ICIDs were the only uncloneable identifiers known [130]. Therefore, IC developers employed special measures to prevent the source data for the
programmable part from being copied by anyone to other chips, which protects
microcircuits from possible malicious attacks aimed at copying (redesigning) them.
The analysis results provided in [128, 129] demonstrate that it is theoretically
possible to achieve a fairly high quantity of such rearrangements with very low
financial costs. One of the disadvantages of the presented hardware metering method,
which is evident to the experts, consists in additional financial and timing costs
of introducing such programmable part of the circuit in ASIC chips, since it will
require the use of additional operations with masks, leading to additional financial
costs. Moreover, two evident variants of the results of such IC analysis are presented
in literature: (1) the first series of analyses performed answers the question: “How
many such experiments will be required to make a conclusion about the absence of
any unauthorized components in the examined microcircuit with a certain level of
reliability?”; 2) repeated series of analyses shall be aimed at assessing the specific
quantity of unauthorized copies of IC chips made by intruders if replicated chips are
actually found in the microcircuit market.
Below we are going to take a brief look at the analysis of two possible versions
of further effects.
(1) Assume that the design center of the ordered microcircuits demands the foundry
to produce no more than n copies, while the foundry actually produces N chips,
where N » n. If a foundry produces k—1 illegal copies of such chip, the total
quantity of such potential ICs will be N = k n. It should be noted that, according
to authoritative experts, a pirate foundry has a better chance of staying undetected if only an equal number of copies of each original chip are produced.
Actually, if we extract l from N objects consisting of k copies of separate designs,
the probability of absence of duplication will be expressed as follows [116]:
Prob [n, k, l] =
1 −
k − 1
N − 1
·
1 −
2(k − 1)
N − 2
· ··
1 −
(l − 1)(k − 1)
N − l − l
However, it is necessary to remember that the upper threshold of this quantity will
be determined by the following expression:
Prob [n, k, l] ≤
1 −
p
n
·
1 −
2 p
n
· · ·
1 −
(l − 1) · p
n
,
where p = 1—1/k.
For developers who failed their math exams during school studies, it is necessary to
provide certain explanations that will help the readers examine this issue more deeply