Scalable formal verification of finite field arithmetic circuits using computer algebra techniques

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Title Scalable formal verification of finite field arithmetic circuits using computer algebra techniques
Publication Type dissertation
School or College College of Engineering
Department Electrical & Computer Engineering
Author Lv, Jinpeng
Date 2012-12
Description With the spread of internet and mobile devices, transferring information safely and securely has become more important than ever. Finite fields have widespread applications in such domains, such as in cryptography, error correction codes, among many others. In most finite field applications, the field size - and therefore the bit-width of the operands - can be very large. The high complexity of arithmetic operations over such large fields requires circuits to be (semi-) custom designed. This raises the potential for errors/bugs in the implementation, which can be maliciously exploited and can compromise the security of such systems. Formal verification of finite field arithmetic circuits has therefore become an imperative. This dissertation targets the problem of formal verification of hardware implementations of combinational arithmetic circuits over finite fields of the type F2k . Two specific problems are addressed: i) verifying the correctness of a custom-designed arithmetic circuit implementation against a given word-level polynomial specification over F2k ; and ii) gate-level equivalence checking of two different arithmetic circuit implementations. This dissertation proposes polynomial abstractions over finite fields to model and represent the circuit constraints. Subsequently, decision procedures based on modern computer algebra techniques - notably, Gr¨obner bases-related theory and technology - are engineered to solve the verification problem efficiently. The arithmetic circuit is modeled as a polynomial system in the ring F2k [x1, x2, · · · , xd], and computer algebrabased results (Hilbert's Nullstellensatz) over finite fields are exploited for verification. Using our approach, experiments are performed on a variety of custom-designed finite field arithmetic benchmark circuits. The results are also compared against contemporary methods, based on SAT and SMT solvers, BDDs, and AIG-based methods. Our tools can verify the correctness of, and detect bugs in, up to 163-bit circuits in F2163 , whereas contemporary approaches are infeasible beyond 48-bit circuits.
Type Text
Publisher University of Utah
Subject Computer Algebra; Cryptography circuits; Equivalence checking; Finite field; Grobner Bases
Dissertation Institution University of Utah
Dissertation Name Doctor of Philosophy
Language eng
Rights Management Copyright © Jinpeng Lv 2012
Format application/pdf
Format Medium application/pdf
Format Extent 1,270,099 bytes
ARK ark:/87278/s64m9kds
Setname ir_etd
ID 195765
Reference URL https://collections.lib.utah.edu/ark:/87278/s64m9kds
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