Computers sometimes use brute force. Hacking programs use so-called brute-force attacks to try out all possible character combinations to guess passwords. CAPTCHAs are therefore intended as an additional safeguard the input of which originates from a human being and not from a machine.
The CAPTCHA is a snapshot of a dynamic, chaotic Hamiltonian system in two dimensions. For the sake of simplicity, his image can be imagined as a grey-scale pixel matrix, where every pixel represents an oscillator. The oscillators are coupled in a network. Every oscillator oscillates between two states and is affected by the neighbouring oscillators as it does so, thus resulting in the grey scales.
The physicists then leave the system to develop chaotically for a period of time. The grey-scale matrix changes the colour of its pixels. The result is an image that no longer contains a recognizable word. The researchers subsequently encrypt this image with the combination of characters and save the result. "We therefore talk of a password-protected CAPTCHA or p-CAPTCHA," says Sergej Flach, who teamed up with Tetyana Laptyeva to achieve the decisive research results at the Max Planck Institute for the Physics of Complex Systems. Since the chaotic evolution of the initial image is deterministic, i.e. reversible, the whole procedure can be reversed using the combination of characters, so that the user can again read the password hidden in the CAPTCHA.
The character combination we use to encrypt the password in the CAPTCHA can be very easy to remember. We thus take account of the fact that most people only want to, or can only, remember simple passwords. The fact that the passwords are correspondingly weak is now no longer important, because the real protection comes from the encrypted password in the CAPTCHA.
On the one hand, the password hidden in the CAPTCHA is too long for computers to be able to guess it using a brute-force attack in a reasonable length of time. On the other, the physicists use a critical system to generate the password image. This system is close to a phase transition: with a phase transition, the system changes from one physical state to another, from the paramagnetic to the ferromagnetic state, for example. Close to the transition, regions repeatedly form which temporarily have already completed the transition. The resulting image is always very grainy. Therefore, a computer cannot distinguish it from the original it is searching for.
The CAPTCHA is a snapshot of a dynamic, chaotic Hamiltonian system in two dimensions. For the sake of simplicity, his image can be imagined as a grey-scale pixel matrix, where every pixel represents an oscillator. The oscillators are coupled in a network. Every oscillator oscillates between two states and is affected by the neighbouring oscillators as it does so, thus resulting in the grey scales.
The physicists then leave the system to develop chaotically for a period of time. The grey-scale matrix changes the colour of its pixels. The result is an image that no longer contains a recognizable word. The researchers subsequently encrypt this image with the combination of characters and save the result. "We therefore talk of a password-protected CAPTCHA or p-CAPTCHA," says Sergej Flach, who teamed up with Tetyana Laptyeva to achieve the decisive research results at the Max Planck Institute for the Physics of Complex Systems. Since the chaotic evolution of the initial image is deterministic, i.e. reversible, the whole procedure can be reversed using the combination of characters, so that the user can again read the password hidden in the CAPTCHA.
The character combination we use to encrypt the password in the CAPTCHA can be very easy to remember. We thus take account of the fact that most people only want to, or can only, remember simple passwords. The fact that the passwords are correspondingly weak is now no longer important, because the real protection comes from the encrypted password in the CAPTCHA.
On the one hand, the password hidden in the CAPTCHA is too long for computers to be able to guess it using a brute-force attack in a reasonable length of time. On the other, the physicists use a critical system to generate the password image. This system is close to a phase transition: with a phase transition, the system changes from one physical state to another, from the paramagnetic to the ferromagnetic state, for example. Close to the transition, regions repeatedly form which temporarily have already completed the transition. The resulting image is always very grainy. Therefore, a computer cannot distinguish it from the original it is searching for.
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