w-asym - Chapter 11 Asymmetric Encryption The setting of...

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Chapter 11 Asymmetric Encryption The setting of public-key cryptography is also called the “asymmetric” setting due to the asymmetry in key information held by the parties. Namely one party has a secret key while another has the public key that matches this secret key. This is in contrast to the symmetry in the private key setting, where both parties had the same key. Asymmetric encryption is thus another name for public-key encryption, the mechanism for achieving data privacy in the public key or asymmetric setting. Our study of asymmetric encryption (following our study of other primitives) will begin by searching for appropriate notions of security, and models and formalizations via which they are captured. We then consider constructions, where we look at how to design and analyze various schemes. With regard to notions of security, we will be able to build considerably on our earlier study of symmetric encryption. Indeed, from this point of view there is very little difference between symmetric and asymmetric encryption; not much more than the fact that in the latter the adversary gets the public key as input. This is important (and re-assuring) to remember. All the intuition and examples we have studied before carry over, so that we enter the study of asymmetric encryption already having a good idea of what encryption is, how security is modeled, and what it means for a scheme to be secure. Accordingly we will deal with the security issues quite briefly, just re-formulating the definitions we have seen before. The second issue (namely constructions) is a different story. Designs of asymmetric encryption schemes rely on tools and ideas different from those underlying the design of symmetric encryp- tion schemes. Namely in the asymmetric case, the basis is (typically) computationally intractable problems in number theory, while for the symmetric case we used block ciphers. Thus, the greater part of the effort in this chapter will be on schemes and their security properties. 11.1 Asymmetric encryption schemes An asymmetric encryption scheme is just like a symmetric encryption scheme except for an asym- metry in the key structure. The key pk used to encrypt is different from the key sk used to decrypt. Furthermore pk is public, known to the sender and also to the adversary. So while only a receiver in possession of the secret key can decrypt, anyone in possession of the corresponding public key can encrypt data to send to this one receiver.
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2 ASYMMETRIC ENCRYPTION Definition 11.1.1 An asymmetric encryption scheme AE = ( K , E , D ) consists of three algorithms, as follows: The randomized key generation algorithm K (takes no inputs and) returns a pair ( pk , sk ) of keys, the public key and matching secret key, respectively. We write ( pk , sk ) $ ←K for the operation of executing K and letting ( pk , sk ) be the pair of keys returned.
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