Encodings of Turing machines in linear logic

Clift, James; Murfet, Daniel

doi:10.1017/s0960129520000109

Cited by 3 publications

(6 citation statements)

References 14 publications

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“…The foremost reason is that while the key-bits in traditional logic locking simply represent a value that the attacker attempts to recover, the bit-sequence in HOLL is an encoding of a program [16,36]. This raw bit-sequence used to program an eFPGA is too "low-level" to be synthesized directly-the size of such bit-streams is about 60-85 times of the keys used in traditional logic locking (128 key bit-sequence).…”

Section: Discussionmentioning

confidence: 99%

“…However, such a configuration bit-sequence represents a function, as compared to the key bits in traditional logic locking that simply represent a value. While any function can be encoded as a bit-sequence [16,36], inferring a function bit-sequence is a computationally much harder problem (a second-order problem) as compared to inferring a value bit-sequence (a first-order problem). In the case of functions, only a complete configuration bit recovery allows the attacker to unlock the function.…”

Section: Hardware Implementationmentioning

confidence: 99%

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HOLL: Program Synthesis for Higher OrderLogic Locking

Takhar¹,

Karri²,

Pilato³

et al. 2022

Preprint

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Logic locking "hides" the functionality of a digital circuit to protect it from counterfeiting, piracy, and malicious design modifications. The original design is transformed into a "locked" design such that the circuit reveals its correct functionality only when it is "unlocked" with a secret sequence of bits-the key bit-string. However, strong attacks, especially the SAT attack that uses a SAT solver to recover the key bitstring, have been profoundly effective at breaking the locked circuit and recovering the circuit functionality. We lift logic locking to Higher Order Logic Locking (HOLL) by hiding a higher-order relation, instead of a key of independent values, challenging the attacker to discover this key relation to recreate the circuit functionality. Our technique uses program synthesis to construct the locked design and synthesize a corresponding key relation. HOLL has low overhead and existing attacks for logic locking do not apply as the entity to be recovered is no more a value. To evaluate our proposal, we propose a new attack (SynthAttack ) that uses an inductive synthesis algorithm guided by an operational circuit as an input-output oracle to recover the hidden functionality. SynthAttack is inspired by the SAT attack, and similar to the SAT attack, it is verifiably correct, i.e., if the correct functionality is revealed, a verification check guarantees the same. Our empirical analysis shows that SynthAttack can break HOLL for small circuits and small key relations, but it is ineffective for real-life designs.

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Section: Discussionmentioning

confidence: 99%

Section: Hardware Implementationmentioning

confidence: 99%

HOLL: Program Synthesis for Higher OrderLogic Locking

Takhar¹,

Karri²,

Pilato³

et al. 2022

Preprint

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show abstract

“…In the naive Bayesian probabilistic extension, we relax the state to a distribution over the states, and the symbols on the tape to distributions over symbols. We then specify a smooth step function which propagates uncertainty according to the independence assumptions discussed in [CM19]. The language of tensor products provides a natural setting for the constructions to follow, so we formulate our definition in this language and verify (Claim 2.1) that we recover the probability update rules of [JCW21, Definition F.1].…”

Section: Smooth Relaxationmentioning

confidence: 99%

“…The absence of this conditioning corresponds to the further assumption that the move direction and write symbol are conditionally independent. The reader seeking a fuller explanation of this may wish to consult Section 6.2 of [CM19] and compare the equations with the lemma that follows.…”

Section: Smooth Relaxationmentioning

confidence: 99%

“…In [CM19], Clift and Murfet, via ideas from differential linear logic, arrive at a particular means of propagating uncertainty through a Turing machine (TM), interpreted in terms of the state of belief of a naive Bayesian observer. The naive Bayesian observer is distinguished from a standard Bayesian observer by a number of independence assumptions-namely, the independence (in distribution) of the tape entries, the state, and the direction of the tape head movement.…”

Section: Introductionmentioning

confidence: 99%

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Smooth relaxation preserving Turing machines

Xu¹

2021

Preprint

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HOLL: Program Synthesis for Higher Order Logic Locking

Takhar

Karri

Pilato

et al. 2022

Tools and Algorithms for the Construction and Analysis of Systems

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Logic locking “hides” the functionality of a digital circuit to protect it from counterfeiting, piracy, and malicious design modifications. The original design is transformed into a “locked” design such that the circuit reveals its correct functionality only when it is “unlocked” with a secret sequence of bits—the key bit-string. However, strong attacks, especially the SAT attack that uses a SAT solver to recover the key bit-string, have been profoundly effective at breaking the locked circuit and recovering the circuit functionality.We lift logic locking to Higher Order Logic Locking (HOLL) by hiding a higher-order relation, instead of a key of independent values, challenging the attacker to discover this key relation to recreate the circuit functionality. Our technique uses program synthesis to construct the locked design and synthesize a corresponding key relation. HOLL has low overhead and existing attacks for logic locking do not apply as the entity to be recovered is no more a value. To evaluate our proposal, we propose a new attack (SynthAttack) that uses an inductive synthesis algorithm guided by an operational circuit as an input-output oracle to recover the hidden functionality. SynthAttack is inspired by the SAT attack, and similar to the SAT attack, it is verifiably correct, i.e., if the correct functionality is revealed, a verification check guarantees the same. Our empirical analysis shows that SynthAttack can break HOLL for small circuits and small key relations, but it is ineffective for real-life designs.

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Encodings of Turing machines in linear logic

Cited by 3 publications

References 14 publications

HOLL: Program Synthesis for Higher OrderLogic Locking

HOLL: Program Synthesis for Higher OrderLogic Locking

Smooth relaxation preserving Turing machines

HOLL: Program Synthesis for Higher Order Logic Locking

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