On the Strength of the Strong RSA Assumption

Shintaro ITAGAKI  Masahiro MAMBO  Hiroki SHIZUYA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E86-A    No.5    pp.1164-1170
Publication Date: 2003/05/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
strong RSA assumption,  RSA,  algebraic computation,  straight-line program,  

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The strong RSA assumption is an assumption that the following problem is hard to solve: Given an RSA modulus and a ciphertext, find a pair of plaintext and exponent corresponding to them. It differs from the standard RSA assumption in a sense that in the strong version, no exponent is given as an input. The strong RSA assumption is considered to be stronger than the RSA assumption, but their exact relationship is not known. We investigate the strength of the strong RSA assumption and show that the strong RSA assumption restricted to low exponents is equivalent to the assumption that RSA problem is intractable for any low exponent. We also show that in terms of algebraic computation, the strong RSA assumption is properly stronger than the RSA assumption if there exists an RSA modulus n such that gcd((n),3)=1 and RSA problem is intractable.