LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

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174 Ashish Gehani, Thomas LaBean, and John Reif We outline below how the bit-wise XOR operation may be done (see Figure 3). For each bit Mi of the message, we construct a sequence ai that will represent the bit in a longer input sequence. By using suitable linking sequences, we can assemble the message M’s n bits into the sequence a1a2 ...an, whichserves as the scaffold strand for one binary input to the XOR. The further portion of the scaffold strand a ′ 1a′ 2 ...a′ n is created based on random inputs and serves as the one-time-pad. It is assumed that many scaffolds of the form a ′ 1a′ 2 ...a′ n have been initially created, cloned using PCR [2,39] or an appropriate technique, and then separated and stored at both the source and destination points in advance. When encryption needs to occur at the source, the particular scaffold used is noted and communicated using a prefix index tag that both sender and destination know corresponds to a particular scaffold. By introducing the scaffold for the message, the scaffold for the one-timepad, connector tiles and the various sequences needed to complete the tiles, the input portion of the structure shown in Figure 3 forms. We call this the input assembly. This process of creating input scaffolds and assembling tiles on the scaffold has been carried out successfully [26]. Each pair of tiles (corresponding to a pair of binary inputs) in the input assembly creates a slot for the binding of a single output tile. When output tiles are introduced, they bind into appropriate binding slots by the matching of sticky ends. Finally, adding ligase enzyme results in a continuous reporter strand R that runs through the entire assembly. If bi = ai ⊕ a ′ i ,fori =1,...,n, then the reporter R = a1a2 ...an.a ′ 1a ′ 2 ...a ′ n.b1b2 ...bn. The reporter strand is shown as a dotted line in Figure 3. This strand may be extracted by first melting apart the hydrogen bonding between strands and then purifying by polyacrylamide gel electrophoresis. It contains the input message, the encryption key, and the ciphertext all linearly concatenated. The ciphertext can be excised using a restriction endonuclease if a cleavage site is encoded between the a0 and b1 tiles. Alternatively the reporter strand could incorporate a nick at that point by using an unphosphorylated oligo between those tiles. The ciphertext could then be gel purified since its length would be half that of the remaining sequence. This may then be stored in a compact form and sent to a destination. Since XOR is its own inverse, the decryption of a Vernam cipher is effected by applying the identical process as encryption with the same key. Specifically, the b1b2 ...bn is used as one input scaffold, the other is chosen from the stored a ′ 1a′ 2 ...a′ n according to the index indicating which sequence was used as the encryption key. The sequences for tile reconstitution, the connector tiles, and ligase are added. After self-assembly, the reporter strand is excised, purified, cut at the marker and the plain text is extracted. We need to guard against loss of synchronization between the message and the key, which would occur when a bit is spuriously introduced or deleted from either sequence. Some fault tolerance is provided by the use of several nucleotides to represent each bit in the the tiles’ construction. This reduces the probabiliity of such errors.
DNA-based Cryptography 175 Fig. 3. XOR computation by the use of DNA tiles 3 Encrypting Images with DNA Chips and DNA One-Time-Pads 3.1 Overview of Method In this section we outline a system capable of encryption and decryption of input and output data in the form of 2D images recorded using microscopic arrays of DNA on a chip. The system we describe here consists of: a data set to be encrypted, a chip bearing immobilized DNA strands, and a library of one-timepads encoded on long DNA strands as described in Section 2.1. The data set for encryption in this specific example is a 2-dimensional image, but variations on the method may be useful for encoding and encrypting other forms of data or types of information. The DNA chip contains an addressable array of nucleotide sequences immobilized such that multiple copies of a single sequence are grouped together in a microscopic pixel. Such DNA chips are currently commercially available and chemical methods for construction of custom variants are well developed. Further chip details will be given below. Fig. 4. DNA Chip Input/Output: Panel A: Message, Panel B: Encrypted Message, Panel C: Decrypted Message
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Lecture Notes in Computer Science 2
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Nata˘sa Jonoska Gheorghe Păun Grz
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Thomas J. Head
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VIII Preface portant to keep in min
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X Table of Contents Formal Properti
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Solving Graph Problems by P Systems
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where Solving Graph Problems by P S
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Writing Information into DNA Masano
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Writing Information into DNA 25 Ham
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Writing Information into DNA 27 Fig
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Writing Information into DNA 29 Dea
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5 Results 5.1 DNA Code for the Engl
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Writing Information into DNA 33 3.
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Writing Information into DNA 35 101
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Balance Machines: Computing = Balan
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+ .. . + Balance Machines: Computin
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x Balance Machines: Computing = Bal
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1 Balance Machines: Computing = Bal
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Eilenberg P Systems with Symbol-Obj
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2 Definitions Definition 1. A strea
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5 Conclusions Eilenberg P Systems w
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Molecular Tiling and DNA Self-assem
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3 Molecular Self-assembly Processes
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8 Hierarchical Tiling Molecular Til
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References Molecular Tiling and DNA
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On Some Classes of Splicing Languag
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ˆxa ˆby ✬ ✩✬ ✩ a b x y
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The Power of Networks of Watson-Cri
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Fixed Point Approach to Commutation
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Fixed Point Approach to Commutation
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Page 139 and 140: � � � � � Fixed Point App
Page 143 and 144: Remarks on Relativisations and DNA
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Page 157 and 158: Splicing Test Tube Systems 147 (c)
Page 159 and 160: I0 Ai i Splicing Test Tube Systems
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Page 163 and 164: Digital Information Encoding on DNA
Page 177 and 178: DNA-based Cryptography Ashish Gehan
Page 179 and 180: DNA-based Cryptography 169 concern.
Page 181 and 182: DNA-based Cryptography 171 The one-
Page 183: DNA-based Cryptography 173 of DNA t
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Page 191 and 192: DNA-based Cryptography 181 4.4 DNA-
Page 193 and 194: DNA-based Cryptography 183 Fig. 7.
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Page 197 and 198: DNA-based Cryptography 187 30. C. M
Page 199 and 200: Splicing to the Limit Elizabeth Goo
Page 201 and 202: Splicing to the Limit 191 molecular
Page 203 and 204: Splicing to the Limit 193 Discussio
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Page 211 and 212: 6 Conclusion Splicing to the Limit
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Page 227 and 228: n-Insertion on Languages 217 Theore
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order β l Transducers with Program
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Transducers with Programmable Input
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start tile Transducers with Program
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Methods for Constructing Coded DNA
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u u Methods for Constructing Coded
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On the Universality of P Systems wi
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An Algorithm for Testing Structure
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Definition 1. Define the relation
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280 Manfred Kudlek Definition 5. Co
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On Languages of Cyclic Words 283 Th
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On Languages of Cyclic Words 285 No
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On Languages of Cyclic Words 287 Th
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A DNA Algorithm for the Hamiltonian
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Formal Languages Arising from Gene
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A Proof of Regularity for Finite Sp
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--- ◦ ❄ ⊗ γ ✲ A Proof of R
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The Duality of Patterning in Molecu
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The Duality of Patterning in Molecu
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Membrane Computing: Some Non-standa
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where: Membrane Computing: Some Non
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where: Membrane Computing: Some Non
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The P Versus NP Problem Through Cel
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Realizing Switching Functions Using
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Realizing Switching Functions Using
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AND Gate Realizing Switching Functi
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NOR Gate Realizing Switching Functi
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Plasmids to Solve #3SAT Rani Siromo
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Plasmids to Solve #3SAT 363 A comme
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Plasmids to Solve #3SAT 365 from th
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Communicating Distributed H Systems
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Proof Communicating Distributed H S
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Books: Publications by Thomas J. He
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Publications by Thomas J. Head 387
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Publications by Thomas J. Head 389
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LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

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