Cryptanalysis of block ciphers with overdefined systems of equations

Several recently proposed ciphers, for example Rijndael and Serpent, are built with layers of small S-boxes interconnected by linear key-dependent layers. Their security relies on the fact, that the classical methods of cryptanalysis (e.g. linear or differential attacks) are based on probabilistic characteristics, which makes their security grow exponentially with the number of rounds N r r. In this paper we study the security of such ciphers under an additional hypothesis: the S-box can be described by an overdefined system of algebraic equations (true with probability 1). We show that this is true for both Serpent (due to a small size of S-boxes) and Rijndael (due to unexpected algebraic properties). We study general methods known for solving overdefined systems of equations, such as XL from Eurocrypt’00, and show their inefficiency. Then we introduce a new method called XSL that uses the sparsity of the equations and their specific structure. The XSL attack uses only relations true with probability 1, and thus the security does not have to grow exponentially in the number of rounds. XSL has a parameter P, and from our estimations is seems that P should be a constant or grow very slowly with the number of rounds. The XSL attack would then be polynomial (or subexponential) in N r> , with a huge constant that is double-exponential in the size of the S-box. The exact complexity of such attacks is not known due to the redundant equations. Though the presented version of the XSL attack always gives always more than the exhaustive search for Rijndael, it seems to (marginally) break 256-bit Serpent. We suggest a new criterion for design of S-boxes in block ciphers: they should not be describable by a system of polynomial equations that is too small or too overdefined.

Swelling induced finite strain flexure in a rectangular block of an isotropic elastic material

The deformation of a rectangular block into an annular wedge is studied with respect to the state of swelling interior to the block. Nonuniform swelling fields are shown to generate these flexure deformations in the absence of resultant forces and bending moments. Analytical expressions for the deformation fields demonstrate these effects for both incompressible and compressible generalizations of conventional hyperelastic materials. Existing results in the absence of a swelling agent are recovered as special cases.

Comparison of block and event-related experimental designs in diffusion-weighted functional MRI

PURPOSE To compare diffusion-weighted functional magnetic resonance imaging (DfMRI), a novel alternative to the blood oxygenation level-dependent (BOLD) contrast, in a functional MRI experiment. MATERIALS AND METHODS Nine participants viewed contrast reversing (7.5 Hz) black-and-white checkerboard stimuli using block and event-related paradigms. DfMRI (b = 1800 mm/s2 ) and BOLD sequences were acquired. Four parameters describing the observed signal were assessed: percent signal change, spatial extent of the activation, the Euclidean distance between peak voxel locations, and the time-to-peak of the best fitting impulse response for different paradigms and sequences. RESULTS The BOLD conditions showed a higher percent signal change relative to DfMRI; however, event-related DfMRI showed the strongest group activation (t = 21.23, P < 0.0005). Activation was more diffuse and spatially closer to the BOLD response for DfMRI when the block design was used. DfMRIevent showed the shortest TTP (4.4 +/- 0.88 sec). CONCLUSION The hemodynamic contribution to DfMRI may increase with the use of block designs.

Plasma-aided nanofabrication: "plasma-building block" approach

Unique features and benefits of the plasma-aided nanofabrication are considered by using the "plasma-building block" approach, which is based on plasma diagnostics and nanofilm characterization, cross-referenced by numerical simulation of generation and dynamics of building blocks in the gas phase, their interaction with nanostructured surfaces, and ab initio simulation of chemical structure of relevant nanoassemblies. The examples include carbon nanotip microemitter structures, semiconductor quantum dots and nanowires synthesized in the integrated plasma-aided nanofabrication facility.

High mobility top-gate and dual-gate polymer thin-film transistors based on diketopyrrolopyrrole-naphthalene copolymer

In this letter, the performance characteristics of top-gate and dual-gate thin-film transistors (TFTs) with active semiconductor layers consisting of diketopyrrolopyrrole-naphthalene copolymer are described. Optimized top-gate TFTs possess mobilities of up to 1 cm 2 /V s with low contact resistance and reduced hysteresis in air. Dual-gate devices possess higher drive currents as well as improved subthreshold and above threshold characteristics compared to single-gate devices. We also describe the reasons that dual-gate devices result in improved performance. The good stability of this polymer combined with their promising electrical properties make this material a very promising semiconductor for printable electronics.

Characteristics of high-performance ambipolar organic field-effect transistors based on a diketopyrrolopyrrole-benzothiadiazole copolymer

In this paper, we report the device characteristics of ambipolar thin-film transistors (TFTs) based on a diketopyrrolopyrrole-benzothiadiazole copolymer. This polymer semiconductor exhibits the largest comparable electron and hole mobility values in a single organic semiconductor. The key to realizing such high mobility values, which are $0.5&cm}{2}/\hbox{V}̇\hbox{s, is molecular design, i.e., the use of suitable surface treatments of the source/drain contact electrodes and device architectures, particularly top-gate configurations. The subthreshold characteristics of the TFT devices are greatly improved by the use of dual-gate device geometry. We also report the first measurement of the velocity distribution of electron and hole velocities in an ambipolar organic semiconductor.

Design and modification of three-component randomly incorporated copolymers for high performance organic photovoltaic applications

In this study we report the molecular design, synthesis, characterization, and photovoltaic properties of a series of diketopyrrolopyrrole (DPP) and dithienothiophene (DTT) based donor-acceptor random copolymers. The six random copolymers are obtained via Stille coupling polymerization using various concentration ratios of donor to acceptor in the conjugated backbone. Bis(trimethylstannyl)thiophene was used as the bridge block to link randomly with the two comonomers 5-(bromothien-2-yl)-2,5-dialkylpyrrolo[3,4-c]pyrrole-1, 4-dione and 2,6-dibromo-3,5-dipentadecyl-dithieno[3,2-b;2′,3′-d] thiophene. The optical properties of these copolymers clearly reveal a change in the absorption band through optimization of the donor-acceptor ratio in the backbone. Additionally, the solution processability of the copolymers is modified through the attachment of different bulky alkyl chains to the lactam N-atoms of the DPP moiety. Applications of the polymers as light-harvesting and electron-donating materials in solar cells, in conjunction with PCBM as acceptor, show power conversion efficiencies (PCEs) of up to 5.02%.

A high mobility P-type DPP-thieno[3,2-b]thiophene copolymer for organic thin-film transistors

A copolymer comprising 1,4-diketopyrrolo[3,4-c]pyrrole (DPP) and thieno[3,2-b]thiophene moieties, PDBT-co-TT, shows high hole mobility of up to 0.94 cm2 V-1 s-1 in organic thin-film transistors. The strong intermolecular interactions originated from π-π stacking and donor-acceptor interaction lead to the formation of interconnected polymer networks having an ordered lamellar structure, which have established highly efficient pathways for charge carrier transport.

Annealing-free high-mobility diketopyrrolopyrrole-quaterthiophene copolymer for solution-processed organic thin film transistors

A donor-acceptor polymer semiconductor, PDQT, comprising diketopyrrolopyrrole (DPP) and β-unsubstituted quaterthiophene (QT) for organic thin film transistors (OTFTs) is reported. This polymer forms ordered layer-by-layer lamellar packing with an edge-on orientation in thin films even without thermal annealing. The strong intermolecular interactions arising from the fused aromatic DPP moiety and the DPP-QT donor-acceptor interaction facilitate the spontaneous self-assembly of the polymer chains into close proximity and form a large π-π overlap, which are favorable for intermolecular charge hopping. The well-interconnected crystalline grains form efficient intergranular charge transport pathways. The desirable chemical, electronic, and morphological structures of PDQT bring about high hole mobility of up to 0.97 cm2/(V·s) in OTFTs with polymer thin films annealed at a mild temperature of 100 °C and similarly high mobility of 0.89 cm2/(V·s) for polymer thin films even without thermal annealing.

Excited-state dynamics in diketopyrrolopyrrole-based copolymer for organic photovoltaics investigated by transient optical spectroscopy

We investigate the photoexcited state dynamics in a donor-acceptor copolymer, poly{3,6-dithiophene-2-yl-2,5-di(2-octyldodecyl)-pyrrolo[3,4-c]- pyrrole-1,4-dione-alt-naphthalene} (pDPP-TNT), by picosecond fluorescence and femtosecond transient absorption spectroscopies. Timeresolved fluorescence lifetime measurements of pDPP-TNT thin films reveal that the lifetime of the singlet excited state is 185 ± 5 ps and that singlet-singlet annihilation occurs at excitation photon densities above 6 × 1017 photons/cm3. From the results of singlet-singlet annihilation analysis, we estimate that the single-singlet annihilation rate constant is (6.0 ± 0.2) × 109cm3 s-1 and the singlet diffusion length is -7 nm. From the comparison of femtosecond transient absorption measurements and picosecond fluorescence measurements, it is found that the time profile of the photobleaching signal in the charge-transfer (CT) absorption band coincides with that of the fluorescence intensity and there is no indication of long-lived species, which clearly suggests that charged species, such as polaron pairs and triplet excitons, are not effectively photogenerated in the neat pDPP-TNT polymer.

Synthesis, characterization and organic field effect transistor performance of a diketopyrrolopyrrole-fluorenone copolymer

A diketopyrrolopyrrole (DPP) with fluorenone (FN) based low band gap alternating copolymer (PDPPT-alt-FN) has been synthesized via Suzuki coupling. PDPPT-alt-FN exhibits a deep HOMO level with a lower band gap. Fabricated organic thin film transistors using PDPPT-alt-FN as a channel semiconductor show p-channel behaviour with the highest hole mobility of 0.083 cm2 V-1 s-1 measured in air.

A fluorenone based low band gap solution processable copolymer for air stable and high mobility organic field effect transistors

A fluorenone based alternating copolymer (PFN-DPPF) with a furan based fused aromatic moiety has been designed and synthesized. PFN-DPPF exhibits a small band gap with a lower HOMO value. Testing this polymer semiconductor as the active layer in organic thin-film transistors results in hole mobilities as high as 0.15 cm2 V-1 s-1 in air.

A low-bandgap diketopyrrolopyrrole-benzothiadiazole-based copolymer for high-mobility ambipolar organic thin-film transistors

A new, solution-processable, low-bandgap, diketopyrrolopyrrole- benzothiadiazole-based, donor-acceptor polymer semiconductor (PDPP-TBT) is reported. This polymer exhibits ambipolar charge transport when used as a single component active semiconductor in OTFTs with balanced hole and electron mobilities of 0.35 cm2 V-1s-1 and 0.40 cm 2 V-1s-1, respectively. This polymer has the potential for ambipolar transistor-based complementary circuits in printed electronics.