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Improved Results on Factoring General RSA Moduli with Known Bits
Factorization General RSA moduli Known bits Integer method
2018/6/25
We revisit the factoring with known bits problem on general RSA moduli in the forms of N=prqsN=prqs for r,s≥1r,s≥1, where two primes pp and qq are of the same bit-size. The relevant moduli are inclusi...
Hashing solutions instead of generating problems: On the interactive certification of RSA moduli
RSA parameter validation zero-knowledge proofs
2018/1/12
Certain RSA-based protocols, for instance in the domain of group signatures, require a prover to convince a verifier that a set of RSA parameters is well-structured (e.g., that the modulus is the prod...
Adversary-dependent Lossy Trapdoor Function from Hardness of Factoring Semi-smooth RSA Subgroup Moduli
factoring assumption semi-smooth RSA subgroup modulus lossy trapdoor function
2016/6/6
Lossy trapdoor functions (LTDFs), proposed by Peikert and Waters (STOC'08), are known to have a number of applications in cryptography. They have been constructed based on various assumptions, which i...
In this paper, we study the problem of factoring an RSA
modulus N = pq in polynomial time, when p is a weak prime, that is, p
can be expressed as ap = u0 + M1u1 + . . . + Mkuk for some k integers
M...
We present three attacks on the Prime Power RSA with modulus N=prq. In the first attack, we consider a public exponent e satisfying an equation ex−ϕ(N)y=z where ϕ(N)=pr−1(p−...
Modular multiplication and modular reduction are the atomic
constituents of most public-key cryptosystems. Amongst the numerous
algorithms for performing these operations, a particularly elegant met...
Results on polynomial interpolation with mixed modular operations and unknown moduli
mixed modular operations unknown moduli
2015/12/22
Motivated by a recently introduced HIMMO key predistribution scheme, we
investigate the limits of various attacks on the polynomial interpolation problem with mixed
modular operations and hidden mod...
Computing genus 2 curves from invariants on the Hilbert moduli space
public-key cryptography Hyperelliptic curve cryptography
2010/5/17
We give a new method for generating genus 2 curves over a finite field with a given number of points on the Jacobian of the curve. We define two new invariants for genus 2 curves as values of modular ...
Let n = pq > q3 be an rsa modulus. This note describes a lll-based
method allowing to factor n given 2 log2 q contiguous bits of p, irrespective to their po-
sition. A second method is presented, wh...