A Continued Fraction-Hyperbola based Attack on RSA cryptosystem
share
In this paper we present new arithmetical and algebraic results following the work of Babindamana and al. on hyperbolas and describe from the new results an approach to attacking a RSA-type modulus based on continued fractions, independent and not bounded by the size of the private key d nor public exponent e compared to Wiener's attack. When successful, this attack is bounded by 𝒪( blogα_j4log(α_i3+α_j3)) with b=10^y, α_i3+α_j3 a non trivial factor of n and α_j4 such that (n+1)/(n-1)=α_i4/α_j4. The primary goal of this attack is to find a point X_α=(-α_3, α_3+1 ) ∈ℤ^2_⋆ that satisfies ⟨ X_α_3, P_3⟩ =0 from a convergent of α_i4/α_j4+δ, with P_3∈ℬ_n(x, y)_|_x≥ 4n. We finally present some experimental examples. We believe these results constitute a new direction in RSA Cryptanalysis using continued fractions.
READ FULL TEXT