5,056 research outputs found
Improved Factoring Attacks on Multi-Prime RSA with Small Prime Difference
In this paper, we study the security of multi-prime RSA with small prime difference and propose two improved factoring attacks. The modulus involved in this variant is the product of r distinct prime factors of the same bit-size. Zhang and Takagi (ACISP 2013) showed a Fermat-like factoring attack on multi-prime RSA. In order to improve the previous result, we gather more information about the prime factors to derive r simultaneous modular equations. The first attack is to combine all the equations and solve one multivariate equation by generic lattice approaches. Since the equation form is similar to multi-prime Phi-hiding problem, we propose the second attack by applying the optimal linearization technique. We also show that our attacks can achieve better bounds in the experiments
Software Grand Exposure: SGX Cache Attacks Are Practical
Side-channel information leakage is a known limitation of SGX. Researchers
have demonstrated that secret-dependent information can be extracted from
enclave execution through page-fault access patterns. Consequently, various
recent research efforts are actively seeking countermeasures to SGX
side-channel attacks. It is widely assumed that SGX may be vulnerable to other
side channels, such as cache access pattern monitoring, as well. However, prior
to our work, the practicality and the extent of such information leakage was
not studied.
In this paper we demonstrate that cache-based attacks are indeed a serious
threat to the confidentiality of SGX-protected programs. Our goal was to design
an attack that is hard to mitigate using known defenses, and therefore we mount
our attack without interrupting enclave execution. This approach has major
technical challenges, since the existing cache monitoring techniques experience
significant noise if the victim process is not interrupted. We designed and
implemented novel attack techniques to reduce this noise by leveraging the
capabilities of the privileged adversary. Our attacks are able to recover
confidential information from SGX enclaves, which we illustrate in two example
cases: extraction of an entire RSA-2048 key during RSA decryption, and
detection of specific human genome sequences during genomic indexing. We show
that our attacks are more effective than previous cache attacks and harder to
mitigate than previous SGX side-channel attacks
Formal Analysis of CRT-RSA Vigilant's Countermeasure Against the BellCoRe Attack: A Pledge for Formal Methods in the Field of Implementation Security
In our paper at PROOFS 2013, we formally studied a few known countermeasures
to protect CRT-RSA against the BellCoRe fault injection attack. However, we
left Vigilant's countermeasure and its alleged repaired version by Coron et al.
as future work, because the arithmetical framework of our tool was not
sufficiently powerful. In this paper we bridge this gap and then use the same
methodology to formally study both versions of the countermeasure. We obtain
surprising results, which we believe demonstrate the importance of formal
analysis in the field of implementation security. Indeed, the original version
of Vigilant's countermeasure is actually broken, but not as much as Coron et
al. thought it was. As a consequence, the repaired version they proposed can be
simplified. It can actually be simplified even further as two of the nine
modular verifications happen to be unnecessary. Fortunately, we could formally
prove the simplified repaired version to be resistant to the BellCoRe attack,
which was considered a "challenging issue" by the authors of the countermeasure
themselves.Comment: arXiv admin note: substantial text overlap with arXiv:1401.817
A Unified Method for Private Exponent Attacks on RSA using Lattices
International audienceLet (n = pq, e = n^β) be an RSA public key with private exponent d = n^δ , where p and q are large primes of the same bit size. At Eurocrypt 96, Coppersmith presented a polynomial-time algorithm for finding small roots of univariate modular equations based on lattice reduction and then succussed to factorize the RSA modulus. Since then, a series of attacks on the key equation ed − kφ(n) = 1 of RSA have been presented. In this paper, we show that many of such attacks can be unified in a single attack using a new notion called Coppersmith's interval. We determine a Coppersmith's interval for a given RSA public key (n, e). The interval is valid for any variant of RSA, such as Multi-Prime RSA, that uses the key equation. Then we show that RSA is insecure if δ < β + 1/3 α − 1/3 √ (12αβ + 4α^2) provided that we have approximation p0 ≥ √ n of p with |p − p0| ≤ 1/2 n^α , α ≤ 1/2. The attack is an extension of Coppersmith's result
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