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x - Faculty of Computer Science - Technische Universität Dresden

x - Faculty of Computer Science - Technische Universität Dresden

Password based

Password based authentication • Enhanced approach using one way (hash) functions User (dog,bone) Server Login Password … … dog h(bone) … … calculates h(bone) ≟ 73 yes grant access no deny access

One-way functions – cryptographic hash functions • One-way function f: – calculating f(x)=y is easy – calculating f -1 (y)=x is hard • computation / storage – open question: Do one-way functions exist? • Cryptographic hash function h – might have different properties depending on the use case – collision resistance: • it is hard to find h(y)=h(x) with y≠x • note: h is usually not collision free, because |h(x)| ≪ |x| – preimage resistance / one-way function / secrecy • given h(x) it is hard to find x – second-preimage resistance / weak collision resistance / binding – Note: • given h(x) it is hard to find h(y)=h(x) with y≠x • h is not necessarily a “random extractor” • only one of “secrecy” and “binding” can be information theoretic secure 74

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