A Unified Method for Private Exponent Attacks on RSA Using Lattices
نویسندگان
چکیده
منابع مشابه
Lattice based Attacks on Small Private Exponent RSA: A Survey
Lattice basis reduction algorithms have contributed a lot to cryptanalysis of RSA crypto system. With coppersmith’s theory of polynomials, these algorithms are searching for the weak instances of Number-theoretic cryptography, mainly RSA. In this paper we present several lattice based attacks on low private exponent of RSA.
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Given knowledge of one or more of the primes in a multiprime RSA modulus we show that the private exponent can be recovered provided it is sufficiently small. In particular, we present a simple and efficient method that given v of the u primes dividing the modulus N recovers any private exponent d satisfying d < Nv/u− . When only one prime is known, this bound can be increased to approximately ...
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In this report, we study the adaptation of existing attacks on short private exponent on fast variants of the well-known RSA public-key cryptosystem, namely the RSA Multiprime and the Takagi family cryptosystems. The first one consists in a variant whose modulus is made up with strictly more than two primes, which permits to quickly decipher or sign using the Chinese Remainder Theorem. The seco...
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We address a lattice based method on small secret exponent attack on RSA scheme. Boneh and Durfee reduced the attack into finding small roots of a bivariate modular equation: x(N+1+y)+1 ≡ 0( mod e), where N is an RSA moduli and e is the RSA public key. Boneh and Durfee proposed a lattice based algorithm for solving the problem. When the secret exponent d is less than N, their method breaks RSA ...
متن کاملLattice based Attacks on Small Private Exponent of RSA: A Survey
Cohen, H. 1995. A Course in Computational Algebraic Number Theory. Springer-Verlag. Second edition. Menezes, A. J, Van Oorschot P. C, and Vanstone. 1997. Hand book of Applied Cryptography. CRC Press. Lenstra A. K, Lenstra Jr. H. W, Lovasz L. 1982. "Factoring polynomials with rational coefficients". Mathematische A1nnalen, volume 261(4): pages 515-534. Rivest R. L, Shamir A, Adleman L....
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ژورنال
عنوان ژورنال: International Journal of Foundations of Computer Science
سال: 2020
ISSN: 0129-0541,1793-6373
DOI: 10.1142/s0129054120500045