Abstract. Strong public-key cryptography is often considered to be too computationally expensive for small devices if not accelerated by cryptographic hardware. We revisited this statement and implemented elliptic curve point multiplication for 160-bit, 192-bit, and 224-bit NIST/SECG curves over GF(p) and RSA-1024 and RSA-2048 on two 8-bit microcontrollers. To accelerate multiple-precision multiplication, we propose a new algorithm to reduce the number of memory accesses. Implementation and analysis led to three observations: 1. Public-key cryptography is viable on small devices without hardware acceleration. On an Atmel ATmega128 at 8 MHz we measured 0.81s for 160-bit ECC point multiplication and 0.43s for a RSA-1024 operation with exponent e = 2 16 + 1. 2. The relative performance advantage of ECC point multiplication over RSA modular exponentiation increases with the decrease in processor word size and the increase in key size. 3. Elliptic curves over fields using pseudo-Mersenne primes as standardized by NIST and SECG allow for high performance implementations and show no performance disadvantage over optimal extension fields or prime fields selected specifically for a particular processor architecture.
The authors thank Day Manoli and Jesse Rothstein for helpful conversations as well as participants at Montana State and Berkeley Demography Brown Bag. This research represents our private research efforts and does not necessarily reflect the views or opinions of the U.S. Department of the Treasury. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulated for discussion and comment purposes. They have not been peerreviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.
The present work focuses on photocatalytic performance
of Ag-TiO2 systems. Nanocrystalline thin films of TiO2-and
Ag-doped TiO2 are grown by sol–gel method, followed
by spin-coating technique on Si ⟨100⟩ surface. The crystallinity
and crystal size were measured from X-ray diffraction and transmission
electron microscopy studies. Lateral distribution of work function
(WF) was examined through contact potential difference measurement
done by scanning Kelvin probe microscopy. Local WFs of Ag-TiO2 thin films were found to be smaller than that of TiO2, and the minimum WF expected from the polynomial curve fitting
was that of pure Ag. The photocatalytic efficiency of these thin films
is estimated from photodegradation of methyl orange analyzed by UV–vis
spectrophotometer. The photodegradation efficiency of Ag-TiO2 nanocrystalline thin films increases up to a certain dopant concentration
of silver, beyond which it decreases. The changes in the photodegradation
efficiency of these films are correlated with variation in contact
potential difference.
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