Relations between arithmetic geometry and public key cryptography

Tamper-Resistant Arithmetic for Public-Key Cryptography

Cryptographic hardware has found many uses in ubiquitous and pervasive security devices with a small form factor, e.g. SIM cards, smart cards, electronic security tokens, and soon even RFIDs. With applications in banking, telecommunication, healthcare, ecommerce and entertainment, these devices use cryptography to provide security services like authentication, identification and confidentiality...

Robust Finite Field Arithmetic for Fault-Tolerant Public-Key Cryptography

We present a new approach to fault tolerant public key cryptography based on redundant arithmetic in finite rings. Redundancy is achieved by embedding non-redundant field or ring elements into larger rings via suitable homomorphisms obtained from modulus scaling. Our approach is closely related to, but not limited by the theory of cyclic binary and arithmetic codes. We present a framework for s...

Studies on Modular Arithmetic Hardware Algorithms for Public-key Cryptography

Public-key cryptography plays an important role in digital communication and storage systems. Processing public-key cryptosystems requires huge amount of computation, and, there is therefore, a great demand for developing dedicated hardware to speed up the computations. In this thesis, we focus on modular arithmetic hardware algorithms for public-key cryptosystem since these two operations are ...

Cryptography. key exchange, public key

General cryptographic schemes are presented where keys can be one-time or ephemeral. Processes for key exchange are derived. Public key cryptographic schemes based on the new systems are established. Authentication and signature schemes are easy to implement. The schemes may be integrated with error-correcting coding schemes so that encryption/coding and decryption/decoding may be done simultan...

Public Key Cryptography