Encriptação com predicados baseada em reticulados

Author(s)

Karina Mochetti de Magalhães

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Computação
• Defense date: 2014-11-27

Examining board members

Ricardo Dahab; Routo Terada; Marcus Vinicius Soledade Poggi de Aragão; Diego de Freitas Aranha; Sueli Irene Rodrigues Costa

• Advisor: Ricardo Dahab; Michel Abdalla

Abstract

In a functional encryption system, an authority holding a master secret key can generate a key that enables the computation of some function on the encrypted data. Then, using the secret key the decryptor can compute the function from the ciphertext. Important examples of functional encryption are Identity-Based Encryption, Attribute-Based Encryption, Inner Product Encryption, Fuzzy Identity-Based Encryption, Hidden Vector Encryption, Certificate-Based Encryption, Public Key Encryption with Keyword Search and Identity-Based Encryption with Wildcards. Predicate encryption schemes are a specialization of functional encryption schemes, in which the function does not give information of the plaintext, but it determines whether the decryption should or should not work properly. Lattice-Based Cryptography is an important alternative to the main cryptographic systems used today, since they are conjectured to be secure against quantum algorithms. Shor's algorithm is capable of solving the Integer Factorization Problem and the Discrete Logarithm Problem in polynomial time on a quantum computer, breaking the most used and important cryptosystems such as RSA, Diffie-Hellman and Elliptic Curve Cryptography. In this work we focus on Lattice-Based Predicate Encryption. We study and describe the main lattice-based schemes found in the literature, extending them to hierarchical versions and showing how the use of ideal lattice affects their security proof. For each scheme, a formal proof of security is detailed, analyses of complexity and variable's size are shown and the parameter's choice ensuring that the decryption works correctly is given (AU)

• FAPESP's process: 09/11071-0 - Cryptographic Post-Quantum Schemes with Special Properties
• Grantee: Karina Mochetti de Magalhães
• Support Opportunities: Scholarships in Brazil - Doctorate