In this paper,we study the RSA cryptosystem with low public key e =Nα and constrained private key d Let μ be a small integer and d ≡ d'modeμ When d' =eγ is sufficiently small and 0 ≤ γ ≤μ-1/8a(1+√9 +...
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In this paper,we study the RSA cryptosystem with low public key e =Nα and constrained private key d Let μ be a small integer and d ≡ d'modeμ When d' =eγ is sufficiently small and 0 ≤ γ ≤μ-1/8a(1+√9 +48a),we show that RSA is vulnerable to cryptanalytic attacks based on lattice basis reduction.
This paper reports new techniques that exploit the security of the prime power moduli N = p(r)q( )(s)using continued fraction method. Our study shows that the key equation ed - k phi(N) = 1 can be exploited using N - ...
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This paper reports new techniques that exploit the security of the prime power moduli N = p(r)q( )(s)using continued fraction method. Our study shows that the key equation ed - k phi(N) = 1 can be exploited using N - 2 r+s/2r N r+s-1/2r + 2r+s-2/2r Nr+s-2/2r as good approximation of phi(N). This enables us to get k/d from the convergents of the continued fractions expansion of a e/N-2 r+s/2r Nr+s-1/2r +2 r+s-2/2r Nr+s-2/2r where the bound of the private exponent is d < 1/2 (N - 2 r+s/2r Nr+s-1/2r + 2r+s-2/2r Nr+s-2/2r) which leads to the polynomial time factorization of the moduli N = p(r)q(s). We further report the polynomial time attacks that can break the security of the generalized prime power moduli N-u = p(u)(r)q(u)(s) using generalized system of equation of the form e(u)d - k(u)phi(N-u) = 1 and e(u)d(u) - k phi(N-u) = 1 by applying simultaneous Diophantine approximations and lll algorithm techniques where 2 <= s < r and u = 1, ..., v.
As internet technology advances and our interactions increasingly take place online, cryptography emerges as a valuable tool to address security concerns. Cryptography serves as a means to guarantee the protection of ...
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As internet technology advances and our interactions increasingly take place online, cryptography emerges as a valuable tool to address security concerns. Cryptography serves as a means to guarantee the protection of privacy and confidential information, thereby instilling confidence when sharing and exchanging such data with other parties. One of the benefits of cryptography is providing confidentiality, which protects our information;either data in transit or data at ease. Three new attacks have been proposed on RSA type modulus N=p2q. The equation eX−NY=Z−(p2k+q2m)Y is the basis for the first attack involves random values of k and m such that k being a multiple of 2 and m being a multiple of 3, both being integers with |p2k+q2m|1/2 and gcd(X,Y)=1. If Z<[Formula presented]N1/3Y and XY<[Formula presented], then by using continued fractions, factoring N can be accomplished within polynomial *** paper also suggested the vulnerabilities t RSA cryptosystem moduli Ns=ps2qs for t≥2 and s=1,…,t for the second and third attack. The attacks are effective if there exists a relationship between t RSA public keys (Nt,et) expressed as esx−Nsys=zs−(ps2k+qs2m)ys or esxs−Nsy=zs−(ps2k+qs2m)y, where the variables x, xs, y, ys, and zs are sufficiently small. The importance lies in the presence of an algorithm that operates within probabilistic polynomial time, which is capable of accepting public parameters as input and yield the factors p and q as output. By employing this algorithm, one can verify whether a key falls within the vulnerable class or not. This characteristic can be valuable when designing a cryptosystem
We explore a fairly generic method to compute roots of polynomials over number fields through complex embeddings. Our main contribution is to show how to use a structure of a relative extension to decode in a subfield...
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We explore a fairly generic method to compute roots of polynomials over number fields through complex embeddings. Our main contribution is to show how to use a structure of a relative extension to decode in a subfield. Additionally we describe several heuristic options to improve practical efficiency. We provide experimental data from our implementation and compare our methods to the state of the art algorithm implemented in Pari/Gp .
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