An important open problem in the area of Traitor Tracing is designing a scheme with constant expansion of the size of keys (users' keys and the encryption key) and of the size of ciphertexts with respect to the size of the plaintext. This problem is known from the introduction of Traitor Tracing by Chor, Fiat and Naor. We refer to such schemes as traitor tracing with constant transmission rate. Here we present a general methodology and two protocol constructions that result in the first two public-key traitor tracing schemes with constant transmission rate in settings where plaintexts can be calibrated to be sufficiently large. Our starting point is the notion of copyrighted function which was presented by Naccache, Shamir and Stern. We first solve the open problem of discrete-log-based and public-key-based copyrighted function. Then, we observe the simple yet crucial relation between (public-key) copyrighted encryption and (public-key) traitor tracing, which we exploit by introducing a generic design paradigm for designing constant transmission rate traitor tracing schemes based on copyrighted encryption functions. Our first scheme achieves the same expansion efficiency as regular ElGamal encryption. The second scheme introduces only a slightly larger (constant) overhead, however, it additionally achieves efficient black-box traitor tracing (against any pirate construction).

Traitor Tracing with constant transmission rate

In order to store a graph or digraph in a computer, we need something other than the diagram or the formal definition. This something is the adjacency matrix, a matrix of O’s and l’s. The l’s correspond to the arcs of the digraph. Certain matrix operations will be seen to correspond to digraph concepts.

Graphs and Matrices

Two secret sharing schemes based on Boolean operations

This book constitutes the refereed proceedings of the 30th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2011, held in Tallinn, Estonia, in May 2011. The 31 papers, presented together with 2 invited talks, were carefully reviewed and selected from 167 submissions. The papers are organized in topical sections on lattice-base cryptography, implementation and side channels, homomorphic cryptography, signature schemes, information-theoretic cryptography, symmetric key cryptography, attacks and algorithms, secure computation, composability, key dependent message security, and public key encryption.

Advances in cryptology : Eurocrypt 2011 : 30th annual international conference on the theory and applications of cryptographic techniques, Tallinn, Estonia, May 15-19, 2011 : proceedings

An image encryption scheme based on rotation matrix bit-level permutation and block diffusion

Chapter 12 presents applications and initiates a study on cryptography. In the modern busy digital world, the word “cryptography” is well known. Every day, knowingly or unknowingly, in many places different techniques of cryptography are used. Starting from the log-in into a PC, sending e-mails, withdrawal of money from an ATM using a PIN code, operating the locker at a bank with the help of a designated person from the bank, sending message using a mobile phone, buying things through the Internet using a credit card, transferring money digitally from one account to another over Internet, every where cryptography is applied. Every such case requires to hide some information or it is necessary to transfer information secretly. So cryptography has something to do with security. Naturally, the questions that come are: What is cryptography? How important is it in daily life? In this chapter, cryptography is introduced and a brief overview of the subject with its basic goal is presented both intuitively and mathematically. More precisely, various cryptographic notions starting from the historical ciphers to modern cryptographic notions like public-key encryption schemes, signature schemes, secret sharing schemes, oblivious transfer etc. by using mathematical tools mainly based on modern algebra are explained. Finally, the implementation issues of three public key cryptographic schemes, namely RSA, ElGamal and Rabin, using the open source software SAGE are discussed.

Introduction to Mathematical Cryptography

An efficient multi-use multi-secret sharing scheme based on hash function

On the security analysis of an image scrambling encryption of pixel bit and its improved scheme based on self-correlation encryption

Basic Modern Algebra with Applications

In this paper we propose a new scheme for a (2,n)-visual threshold scheme (VTS) for color images. Our scheme achieves a better color ratio than the schemes proposed by Koga et al in 1998 and 2001. The pixel expansion of our scheme is reasonably good and we also give a lower bound on the color ratio of our scheme.

Avishek Adhikari

Papers

Introduction to Mathematical Cryptography

An efficient multi-use multi-secret sharing scheme based on hash function

On the security analysis of an image scrambling encryption of pixel bit and its improved scheme based on self-correlation encryption

Basic Modern Algebra with Applications

A New (2, n )-Visual Threshold Scheme for Color Images