ID-based Cryptography from Composite Degree Residuosity

We present identity-based identification (resp. encryption, signature, blind signature,ring signature) from composite degree residuosity (CDR). Constructions of identifications and signatures motivated by several existing CDR-based bandwidth-efficient encryption schemes are presented. Their securities are proven equivalent to famous hard problems, in the random oracle model. Motivated by Cocks,we construct an identity-based encryption from CDR. Its security is proven equivalent to a new problem, the JSR (Jacobi Symbol of Roots of two quadratic polynomials) Problem. We prove JSR is at least as hard as QRP (Quadratic Residuosity Problem). Furthermore, we present the first two-way equivalence reduction of the security of Cocks\u27 IBE, to the JSR Problem

Identity-based cryptography from paillier cryptosystem.

Au Man Ho Allen.Thesis (M.Phil.)--Chinese University of Hong Kong, 2005.Includes bibliographical references (leaves 60-68).Abstracts in English and Chinese.Abstract --- p.iAcknowledgement --- p.iiiChapter 1 --- Introduction --- p.1Chapter 2 --- Preliminaries --- p.5Chapter 2.1 --- Complexity Theory --- p.5Chapter 2.2 --- Algebra and Number Theory --- p.7Chapter 2.2.1 --- Groups --- p.7Chapter 2.2.2 --- Additive Group Zn and Multiplicative Group Z*n --- p.8Chapter 2.2.3 --- The Integer Factorization Problem --- p.9Chapter 2.2.4 --- Quadratic Residuosity Problem --- p.11Chapter 2.2.5 --- Computing e-th Roots (The RSA Problem) --- p.13Chapter 2.2.6 --- Discrete Logarithm and Related Problems --- p.13Chapter 2.3 --- Public key Cryptography --- p.16Chapter 2.3.1 --- Encryption --- p.17Chapter 2.3.2 --- Digital Signature --- p.20Chapter 2.3.3 --- Identification Protocol --- p.22Chapter 2.3.4 --- Hash Function --- p.24Chapter 3 --- Paillier Cryptosystems --- p.26Chapter 3.1 --- Introduction --- p.26Chapter 3.2 --- The Paillier Cryptosystem --- p.27Chapter 4 --- Identity-based Cryptography --- p.30Chapter 4.1 --- Introduction --- p.31Chapter 4.2 --- Identity-based Encryption --- p.32Chapter 4.2.1 --- Notions of Security --- p.32Chapter 4.2.2 --- Related Results --- p.35Chapter 4.3 --- Identity-based Identification --- p.36Chapter 4.3.1 --- Security notions --- p.37Chapter 4.4 --- Identity-based Signature --- p.38Chapter 4.4.1 --- Security notions --- p.39Chapter 5 --- Identity-Based Cryptography from Paillier System --- p.41Chapter 5.1 --- Identity-based Identification schemes in Paillier setting --- p.42Chapter 5.1.1 --- Paillier-IBI --- p.42Chapter 5.1.2 --- CGGN-IBI --- p.43Chapter 5.1.3 --- GMMV-IBI --- p.44Chapter 5.1.4 --- KT-IBI --- p.45Chapter 5.1.5 --- Choice of g for Paillier-IBI --- p.46Chapter 5.2 --- Identity-based signatures from Paillier system . . --- p.47Chapter 5.3 --- Cocks ID-based Encryption in Paillier Setting . . --- p.48Chapter 6 --- Concluding Remarks --- p.51A Proof of Theorems --- p.53Chapter A.1 --- "Proof of Theorems 5.1, 5.2" --- p.53Chapter A.2 --- Proof Sketch of Remaining Theorems --- p.58Bibliography --- p.6

Cryptography from Post-Quantum Assumptions

In this thesis we present our contribution in the field of post-quantum cryptography. We introduce a new notion of {\em weakly Random-Self-Reducible} public-key cryptosystem and show how it can be used to implement secure Oblivious Transfer. We also show that two recent (Post-quantum) cryptosystems can be considered as {\em weakly Random-Self-Reducible}. We introduce a new problem called Isometric Lattice Problem and reduce graph isomorphism and linear code equivalence to this problem. We also show that this problem has a perfect zero-knowledge interactive proof with respect to a malicious verifier; this is the only hard problem in lattices that is known to have this property