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Download PDF by Raphael Pass, Abhi Shelat: A Course in Cryptography

By Raphael Pass, Abhi Shelat

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Additional resources for A Course in Cryptography

Example text

There are several ways that the notion of one-wayness can be defined formally. We start with a definition that formalizes our intuition in the simplest way. 1 (Worst-case One-way Function). 2. One-Way Functions 27 1. Easy to compute. t. C that computes f ( x ) on all inputs x ∈ {0, 1}∗ , and 2. ). , those where inverting the function for most x values is easy, but every machine fails to invert f ( x ) for infinitely many x’s. It is an open question whether such functions can still be used for good encryption schemes.

This includes secret-sharing protocols and secure two-party (or multi-party) computation protocols. We have described the later earlier in this chapter; secret-sharing protocols are methods which allow a set of n parties to receive “shares” of a secret with the property that any “small” subset of shares leaks no information about the secret, but once an appropriate number of shares are collected the whole secret can be recovered. Composability. It turns out that cryptographic schemes that are secure when executed in isolation can be completely compromised if many instances of the scheme are simultaneously executed (as is unavoidable when executing cryptographic protocols in modern networks).

Indistinguishability. The notion of indistinguishability formalizes what it means for a computationally-bounded adversary to be unable to “tell apart” two distributions. This notion is central to modern definitions of security for encryption schemes, but also for formally defining notions such as pseudo-random generation, commitment schemes, zero-knowledge protocols, etc. Knowledge. A central desideratum in the design of cryptographic protocols is to ensure that the protocol execution does not leak more “knowledge” than what is necessary.

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A Course in Cryptography by Raphael Pass, Abhi Shelat


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