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Master's Dissertation
DOI
10.11606/D.45.2013.tde-13082014-141746
Document
Author
Full name
Reynaldo Caceres Villena
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2013
Supervisor
Committee
Terada, Routo (President)
Campos, Geraldo Lino de
Gubitoso, Marco Dimas
Title in Portuguese
Reconstrução da chave secreta do RSA multi-primo
Keywords in Portuguese
ataques cold-boot
criptossistema RSA multi-primo
reconstrução da chave secreta
Abstract in Portuguese
Em 2009, N. Heninger e H. Shacham apresentaram um algoritmo de reconstrução que permite recuperar a chave secreta sk do criptossistema RSA básico em tempo polinomial tendo em forma aleatória 27 % dos seus bits. Sabemos que podemos obter uma versão com erros (bits modicados) da chave secreta RSA graças aos ataques cold boot. O algoritmo apresentado por Heninger-Shacham corrige esses erros fazendo uso das relações matemáticas que existe entre as chaves pública e secreta do criptossistema RSA básico. O objetivo deste trabalho é estudar esse algoritmo para implementar e analisar seu análogo para o criptossistema RSA multi-primo. Os resultados obtidos mostram que para reconstruir a chave secreta sk do criptossistema RSA u-primos é preciso ter uma fração de bits corretos maior a 2 - 2^((u+2)/(2u+1)), mostrando assim que a segurança oferecida pelo criptossistema RSA multi-primo (u>/ 3) é maior com relação ao criptossistema RSA básico (u = 2).
Title in English
Reconstructing the secret key of RSA multi-prime
Keywords in English
cold boot attacks
multi-prime RSA cryptosystem
secret key reconstructing
Abstract in English
In 2009, N. Heninger and H. Shacham presented an algoritm for reconstructing the secret key sk of the basic RSA cryptosystem in polynomial time With a fraction of random bits greater or equal to 0.27 of its bits. We know that secret key with errors sk can be obtained from DRAM using cold-boot attacks. The Heninger and Shacham's algorithm xes these errors using the redundancy of secret and public key of basic RSA cryptosystem. In this work, the topic is to study this algoritm to implement and analyze its analogous for the multi-prime RSA cryptosystem. Our obtained results show the secret key sk of multi-prime RSA cryptosystem can be Reconstructed having a fraction equal or greater than 2 - 2^((u+2)/(2u+1)) of random bits. therefore the security of multi-prime RSA cryptosystem (u >/ 3) is greater than basic RSA cryptosystem (u = 2).
 
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Tese_7259609.pdf (1.22 Mbytes)
Publishing Date
2014-11-03
 
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