Introduction to Security Reduction

This monograph illustrates important notions in security reductions and essential techniques in security reductions for group-based cryptosystems. Using digital signatures and encryption as examples, the authors explain how to program correct security reductions for those cryptographic primitives. Various schemes are selected and re-proven in this book to demonstrate and exemplify correct security reductions.

This book is suitable for researchers and graduate students engaged with public-key cryptography.

Notions, Definitions and Models. - Identity-Based Encryption. - Foundations of Group-Based Cryptography. - Foundations of Security Reduction. - Digital Signatures With Random Oracles. - Digital Signatures Without Random Oracles. - Public Key Encryption With Random Oracles. - Public Key Encryption Without Random Oracles. - Identity-Based Encryption With Random Oracles. - Identity-Based Encryption Without Random Oracles.