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Master's Dissertation
DOI
10.11606/D.45.2011.tde-14032012-213011
Document
Author
Full name
Dionathan Nakamura
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2011
Supervisor
Committee
Terada, Routo (President)
Barreto, Paulo Sergio Licciardi Messeder
Hernandez, Julio Cesar Lopez
Title in Portuguese
Segurança do bit menos significativo no RSA e em curvas elípticas
Keywords in Portuguese
Criptografia
Curvas Elípticas
Diffie-Hellman
RSA
Abstract in Portuguese
Sistemas criptográficos como o RSA e o Diffie-Hellman sobre Curvas Elípticas (DHCE) têm fundamento em problemas computacionais considerados difíceis, por exemplo, o problema do logaritmo (PLD) e o problema da fatoração de inteiros (PFI). Diversos trabalhos têm relacionado a segurança desses sistemas com os problemas subjacentes. Também é investigada a segurança do LSB (bit menos significativo) da chave secreta no DHCE (no RSA é o LSB da mensagem) com relação à segurança de toda a chave. Nesses trabalhos são apresentados algoritmos que conseguem inverter os sistemas criptográficos citados fazendo uso de oráculos que predizem o LSB. Nesta dissertação, fazemos a implementação de dois desses algoritmos. Identificamos parâmetros críticos e mudamos a amostragem do formato original. Com essa mudança na amostragem conseguimos uma melhora significativa nos tempos de execução. Um dos algoritmos (ACGS), para valores práticos do RSA, era mais lento que a solução para o PFI, com nosso resultado passou a ser mais veloz. Ainda, mostramos como provas teóricas podem não definir de maneira precisa o tempo de execução de um algoritmo.
Title in English
Least significant bit security of the RSA and elliptic curves
Keywords in English
Cryptography
Diffie-Hellman
Elliptic Curves.
RSA
Abstract in English
Cryptographic systems like RSA and Elliptic Curve Diffie-Hellman (DHCE) is based on computational problems that are considered hard, e.g. the discrete logarithm (PLD) and integer factorization (PFI) problems. Many papers investigated the relationship between the security of these systems to the computational difficulty of the underlying problems. Moreover, they relate the bit security, actually the LSB (Least Significant Bit), of the secret key in the DHCE and the LSB of the message in the RSA, to the security of the whole key. In these papers, algorithms are presented to invert these cryptographic systems making use of oracles that predict the LSB. In this dissertation we implement two of them. Critical parameters are identified and the original sampling is changed. With the modified sampling we achieve an improvement in the execution times. For practical values of the RSA, the algorithm ACGS becomes faster than the PFI. Moreover, we show how theoretical proofs may lead to inaccurate timing estimates.
 
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dissertacao.pdf (609.36 Kbytes)
Publishing Date
2012-03-19
 
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