Asymmetric Leakage from Multiplier and Collision-Based Single-Shot Side-Channel Attack

The single-shot collision attack on RSA proposed by Hanley et al. is studied focusing on the difference between two operands of multiplier. It is shown that how leakage from integer multiplier and long-integer multiplication algorithm can be asymmetric between two operands. The asymmetric leakage is verified with experiments on FPGA and micro-controller platforms. Moreover, we show an experimental result in which success and failure of the attack is determined by the order of operands. Therefore, designing operand order can be a cost-effective countermeasure. Meanwhile we also show a case in which a particular countermeasure becomes ineffective when the asymmetric leakage is considered. In addition to the above main contribution, an extension of the attack by Hanley et al. using the signal-processing technique of Big Mac Attack is presented

Cryptanalysis of Server-Aided RSA Protocols with Private-Key Splitting

International audienceWe analyze the security and the efficiency of interactive protocols where a client wants to delegate the computation of an RSA signature given a public key, a public message and the secret signing exponent. We consider several protocols where the secret exponent is splitted using some algebraic decomposition. We first provide an exhaustive analysis of the delegation protocols in which the client outsources a single RSA exponentiation to the server. We then revisit the security of the protocols RSA-S1 and RSA-S2 that were proposed by Matsumoto, Kato and Imai in 1988. We present an improved lattice-based attack on RSA-S1 and we propose a simple variant of this protocol that provides better efficiency for the same security level. Eventually, we present the first attacks on the protocol RSA-S2 that employs the Chinese Remainder Theorem to speed up the client's computation. The efficiency of our (heuristic) attacks has been validated experimentally

CSI Neural Network: Using Side-channels to Recover Your Artificial Neural Network Information

Machine learning has become mainstream across industries. Numerous examples proved the validity of it for security applications. In this work, we investigate how to reverse engineer a neural network by using only power side-channel information. To this end, we consider a multilayer perceptron as the machine learning architecture of choice and assume a non-invasive and eavesdropping attacker capable of measuring only passive side-channel leakages like power consumption, electromagnetic radiation, and reaction time. We conduct all experiments on real data and common neural net architectures in order to properly assess the applicability and extendability of those attacks. Practical results are shown on an ARM CORTEX-M3 microcontroller. Our experiments show that the side-channel attacker is capable of obtaining the following information: the activation functions used in the architecture, the number of layers and neurons in the layers, the number of output classes, and weights in the neural network. Thus, the attacker can effectively reverse engineer the network using side-channel information. Next, we show that once the attacker has the knowledge about the neural network architecture, he/she could also recover the inputs to the network with only a single-shot measurement. Finally, we discuss several mitigations one could use to thwart such attacks.Comment: 15 pages, 16 figure

On Deterministic Polynomial-time Equivalence of Computing the CRT-RSA Secret Keys and Factoring

Let N = pq be the product of two large primes. Consider Chinese remainder theorem-Rivest, Shamir, Adleman (CRT-RSA) with the public encryption exponent e and private decryption exponents dp, dq. It is well known that given any one of dp or dq (or both) one can factorise N in probabilistic poly(log N) time with success probability almost equal to 1. Though this serves all the practical purposes, from theoretical point of view, this is not a deterministic polynomial time algorithm. In this paper, we present a lattice-based deterministic poly(log N) time algorithm that uses both dp, dq (in addition to the public information e, N) to factorise N for certain ranges of dp, dq. We like to stress that proving the equivalence for all the values of dp, dq may be a nontrivial task.Defence Science Journal, 2012, 62(2), pp.122-126, DOI:http://dx.doi.org/10.14429/dsj.62.171

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

A cryptanalytic attack on the LUC cryptosystem using continued fractions

The LUC cryptosystem is a modification of the RSA cryptosystem based on Lucas sequences. In this paper we extend the Verheul - van Tilborg and Dujella variants of the Wiener attack on RSA to the LUC cryptosystem. We describe an algorithm for finding a secret key $d$ of the form $d = r q_{m+1} pm s q_m$, for some $mgeq -1$ and nonnegative integers $r$ and $s$, using continued fractions. We derive bounds for $r$ and $s$ using results on Diophantine approximations