Physical one-way functions
01 Jan 2001-Science (American Association for the Advancement of Science)-Vol. 297, Iss: 5589, pp 2026-2030
TL;DR: The concept of fabrication complexity is introduced as a way of quantifying the difficulty of materially cloning physical systems with arbitrary internal states as primitives for physical analogs of cryptosystems.
Abstract: Modern cryptography relies on algorithmic one-way functions—numerical functions which are easy to compute but very difficult to invert. This dissertation introduces physical one-way functions and physical one-way hash functions as primitives for physical analogs of cryptosystems.
Physical one-way functions are defined with respect to a physical probe and physical system in some unknown state. A function is called a physical one-way function if (a) there exists a deterministic physical interaction between the probe and the system which produces an output in constant time; (b) inverting the function using either computational or physical means is difficult; (c) simulating the physical interaction is computationally demanding and (d) the physical system is easy to make but difficult to clone.
Physical one-way hash functions produce fixed-length output regardless of the size of the input. These hash functions can be obtained by sampling the output of physical one-way functions. For the system described below, it is shown that there is a strong correspondence between the properties of physical one-way hash functions and their algorithmic counterparts. In particular, it is demonstrated that they are collision-resistant and that they exhibit the avalanche effect, i.e., a small change in the physical system causes a large change in the hash value.
An inexpensive prototype authentication system based on physical one-way hash functions is designed, implemented, and analyzed. The prototype uses a disordered three-dimensional microstructure as the underlying physical system and coherent radiation as the probe. It is shown that the output of the interaction between the physical system and the probe can be used to robustly derive a unique tamper-resistant identifier at a very low cost per bit. The explicit use of three-dimensional structures marks a departure from prior efforts. Two protocols, including a one-time pad protocol, that illustrate the utility of these hash functions are presented and potential attacks on the authentication system are considered.
Finally, the concept of fabrication complexity is introduced as a way of quantifying the difficulty of materially cloning physical systems with arbitrary internal states. Fabrication complexity is discussed in the context of an idealized machine—a Universal Turing Machine augmented with a fabrication head—which transforms algorithmically minimal descriptions of physical systems into the systems themselves. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)
Citations
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04 Jun 2007
TL;DR: This work presents PUF designs that exploit inherent delay characteristics of wires and transistors that differ from chip to chip, and describes how PUFs can enable low-cost authentication of individual ICs and generate volatile secret keys for cryptographic operations.
Abstract: Physical Unclonable Functions (PUFs) are innovative circuit primitives that extract secrets from physical characteristics of integrated circuits (ICs). We present PUF designs that exploit inherent delay characteristics of wires and transistors that differ from chip to chip, and describe how PUFs can enable low-cost authentication of individual ICs and generate volatile secret keys for cryptographic operations.
2,014 citations
Cites methods from "Physical one-way functions"
...For example, Pappu proposed an optical PUF, which uses the speckle patterns of optical medium for laser light [ 12 ]....
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TL;DR: This survey examines approaches proposed by scientists for privacy protection and integrity assurance in RFID systems, and treats the social and technical context of their work.
Abstract: This paper surveys recent technical research on the problems of privacy and security for radio frequency identification (RFID). RFID tags are small, wireless devices that help identify objects and people. Thanks to dropping cost, they are likely to proliferate into the billions in the next several years-and eventually into the trillions. RFID tags track objects in supply chains, and are working their way into the pockets, belongings, and even the bodies of consumers. This survey examines approaches proposed by scientists for privacy protection and integrity assurance in RFID systems, and treats the social and technical context of their work. While geared toward the nonspecialist, the survey may also serve as a reference for specialist readers.
1,994 citations
Cites background from "Physical one-way functions"
...For example, physical one-way functions (POWFs) [ 71 ] are small plastic objects with reflective inclusions such as tiny glass beads....
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Proceedings Article•
01 Jan 2007
1,944 citations
18 Nov 2002
TL;DR: It is argued that a complex integrated circuit can be viewed as a silicon PUF and a technique to identify and authenticate individual integrated circuits (ICs) is described.
Abstract: We introduce the notion of a Physical Random Function (PUF). We argue that a complex integrated circuit can be viewed as a silicon PUF and describe a technique to identify and authenticate individual integrated circuits (ICs).We describe several possible circuit realizations of different PUFs. These circuits have been implemented in commodity Field Programmable Gate Arrays (FPGAs). We present experiments which indicate that reliable authentication of individual FPGAs can be performed even in the presence of significant environmental variations.We describe how secure smart cards can be built, and also briefly describe how PUFs can be applied to licensing and certification applications.
1,644 citations
Cites methods from "Physical one-way functions"
...It is the application that was described in [12]....
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...In previous literature [12] PUFs were referred to as Physical One Way Functions, and realized using 3-dimensional micro-structures and coherent radiation....
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TL;DR: Focusing of coherent light through opaque scattering materials by control of the incident wavefront with a brightness up to a factor of 1000 higher than the brightness of the normal diffuse transmission is reported.
Abstract: We report focusing of coherent light through opaque scattering materials by control of the incident wavefront. The multiply scattered light forms a focus with a brightness that is up to a factor of 1000 higher than the brightness of the normal diffuse transmission.
1,624 citations
References
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Book•
01 Jan 1990TL;DR: The updated new edition of the classic Introduction to Algorithms is intended primarily for use in undergraduate or graduate courses in algorithms or data structures and presents a rich variety of algorithms and covers them in considerable depth while making their design and analysis accessible to all levels of readers.
Abstract: From the Publisher:
The updated new edition of the classic Introduction to Algorithms is intended primarily for use in undergraduate or graduate courses in algorithms or data structures. Like the first edition,this text can also be used for self-study by technical professionals since it discusses engineering issues in algorithm design as well as the mathematical aspects.
In its new edition,Introduction to Algorithms continues to provide a comprehensive introduction to the modern study of algorithms. The revision has been updated to reflect changes in the years since the book's original publication. New chapters on the role of algorithms in computing and on probabilistic analysis and randomized algorithms have been included. Sections throughout the book have been rewritten for increased clarity,and material has been added wherever a fuller explanation has seemed useful or new information warrants expanded coverage.
As in the classic first edition,this new edition of Introduction to Algorithms presents a rich variety of algorithms and covers them in considerable depth while making their design and analysis accessible to all levels of readers. Further,the algorithms are presented in pseudocode to make the book easily accessible to students from all programming language backgrounds.
Each chapter presents an algorithm,a design technique,an application area,or a related topic. The chapters are not dependent on one another,so the instructor can organize his or her use of the book in the way that best suits the course's needs. Additionally,the new edition offers a 25% increase over the first edition in the number of problems,giving the book 155 problems and over 900 exercises thatreinforcethe concepts the students are learning.
21,651 citations
"Physical one-way functions" refers background in this paper
...Excellent (and exhaustive) reviews of this material may be found in Papadimitriou [5], Greenlaw and Hoover [6], and Corman, Leiserson, and Rivest [7]....
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TL;DR: In this paper, it is shown that the difference of information between the approximation of a signal at the resolutions 2/sup j+1/ and 2 /sup j/ (where j is an integer) can be extracted by decomposing this signal on a wavelet orthonormal basis of L/sup 2/(R/sup n/), the vector space of measurable, square-integrable n-dimensional functions.
Abstract: Multiresolution representations are effective for analyzing the information content of images. The properties of the operator which approximates a signal at a given resolution were studied. It is shown that the difference of information between the approximation of a signal at the resolutions 2/sup j+1/ and 2/sup j/ (where j is an integer) can be extracted by decomposing this signal on a wavelet orthonormal basis of L/sup 2/(R/sup n/), the vector space of measurable, square-integrable n-dimensional functions. In L/sup 2/(R), a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi (x). This decomposition defines an orthogonal multiresolution representation called a wavelet representation. It is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters. Wavelet representation lies between the spatial and Fourier domains. For images, the wavelet representation differentiates several spatial orientations. The application of this representation to data compression in image coding, texture discrimination and fractal analysis is discussed. >
20,028 citations
Journal Article•
TL;DR: The Mathematical Theory of Communication (MTOC) as discussed by the authors was originally published as a paper on communication theory more than fifty years ago and has since gone through four hardcover and sixteen paperback printings.
Abstract: Scientific knowledge grows at a phenomenal pace--but few books have had as lasting an impact or played as important a role in our modern world as The Mathematical Theory of Communication, published originally as a paper on communication theory more than fifty years ago. Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings. It is a revolutionary work, astounding in its foresight and contemporaneity. The University of Illinois Press is pleased and honored to issue this commemorative reprinting of a classic.
15,525 citations
TL;DR: This paper suggests ways to solve currently open problems in cryptography, and discusses how the theories of communication and computation are beginning to provide the tools to solve cryptographic problems of long standing.
Abstract: Two kinds of contemporary developments in cryptography are examined. Widening applications of teleprocessing have given rise to a need for new types of cryptographic systems, which minimize the need for secure key distribution channels and supply the equivalent of a written signature. This paper suggests ways to solve these currently open problems. It also discusses how the theories of communication and computation are beginning to provide the tools to solve cryptographic problems of long standing.
14,980 citations
"Physical one-way functions" refers background in this paper
...Public-key encryption of the Diffie-Hellman flavor [9] relies on trapdoor one-way functions, where inversion is efficient given the trapdoor, but intractable otherwise....
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...1 The origin of OWFs and OWHFs One-way functions are central to modern public-key cryptography [9]....
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TL;DR: An encryption method is presented with the novel property that publicly revealing an encryption key does not thereby reveal the corresponding decryption key.
Abstract: An encryption method is presented with the novel property that publicly revealing an encryption key does not thereby reveal the corresponding decryption key. This has two important consequences: (1) Couriers or other secure means are not needed to transmit keys, since a message can be enciphered using an encryption key publicly revealed by the intented recipient. Only he can decipher the message, since only he knows the corresponding decryption key. (2) A message can be “signed” using a privately held decryption key. Anyone can verify this signature using the corresponding publicly revealed encryption key. Signatures cannot be forged, and a signer cannot later deny the validity of his signature. This has obvious applications in “electronic mail” and “electronic funds transfer” systems. A message is encrypted by representing it as a number M, raising M to a publicly specified power e, and then taking the remainder when the result is divided by the publicly specified product, n, of two large secret primer numbers p and q. Decryption is similar; only a different, secret, power d is used, where e * d ≡ 1(mod (p - 1) * (q - 1)). The security of the system rests in part on the difficulty of factoring the published divisor, n.
14,659 citations