Differential cross sections for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>γ</mml:mi><mml:mo>+</mml:mo><mml:mi>p</mml:mi><mml:mo>→</mml:mo><mml:msup><mml:mi>K</mml:mi><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:mi>Y</mml:mi></mml:mrow></mml:math>for Λ and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mi>Σ</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>hyperons

High-statistics cross sections for the reactions $\ensuremath{\gamma}+p\ensuremath{\rightarrow}{K}^{+}+\ensuremath{\Lambda}$ and $\ensuremath{\gamma}+p\ensuremath{\rightarrow}{K}^{+}+{\ensuremath{\Sigma}}^{0}$ have been measured using CLAS at Jefferson Lab for center-of-mass energies W between 1.6 and 2.53 GeV, and for $\ensuremath{-}0.85&lt;\mathrm{cos}{\ensuremath{\theta}}_{{K}^{+}}^{c.m.}&lt;+0.95$. In the ${K}^{+}\ensuremath{\Lambda}$ channel we confirm a resonance-like structure near $W=1.9$ GeV at backward kaon angles. The position and width of this structure change with angle, indicating that more than one resonance is likely playing a role. The ${K}^{+}\ensuremath{\Lambda}$ channel at forward angles and all energies is well described by a t-channel scaling characteristic of Regge exchange, whereas the same scaling applied to the ${K}^{+}{\ensuremath{\Sigma}}^{0}$ channel is less successful. Several existing theoretical models are compared to the data, but none provide a good representation of the results.