Recap of PublicKey Encryption
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Summary
In this chapter, we investigated publickey encryption. We looked at the general problem of designing a publickey cryptosystem and then studied two publickey cryptosystems in some detail. We also looked at how the properties of publickey cryptosystems are most effectively harnessed in applications.
The main issues we covered were the following:

Publickey cryptosystems provide the potential for two entities who do not share a symmetric key to employ cryptography to secure the data they exchange.

Publickey encryption requires the use of a trapdoor oneway function.

RSA is a wellrespected and widely deployed publickey cryptosystem with security based on the belief that factoring in large numbers is difficult.

ElGamal is a publickey cryptosystem with security based on the belief that solving the discrete logarithm problem is difficult.

Variants of ElGamal based on elliptic curves offer the significant benefit that keys are shorter than in either RSA or basic ElGamal.

Publickey cryptosystems are less efficient to operate than most symmetric cryptosystems. As a result, publickey encryption is usually employed in a hybrid encryption process, which exchanges a symmetric key used for bulk data encryption.
The significant advantages to applications made possible by publickey cryptosystems led to a revolution in cryptography in the mid1970s with a further boom in interest following the development of the Internet in the 1990s. However, the publickey cryptosystems in current use are not secure against an adversary with a quantum computer. As a result, there is considerable interest in developing new postquantum publickey cryptosystems, and developments in this area can be expected.
Publickey cryptography, to an extent, ‘solves’ the problem of symmetric key establishment. However, it replaces this problem with that of authenticating public keys. None of the advantages of publickey cryptosystems can be fully exploited unless we have some level of assurance that public keys are indeed associated with the entities to which we believe they belong.
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