Simultaneous Diagonalization of Incomplete Matrices and Applications

We consider the problem of recovering the entries of diagonal matrices $\{U_a\}_a$ for $a = 1,\ldots,t$ from multiple "incomplete" samples $\{W_a\}_a$ of the form $W_a=PU_aQ$, where $P$ and $Q$ are unknown matrices of low rank. We devise practical algorithms for this problem depending on the ranks of $P$ and $Q$. This problem finds its motivation in cryptanalysis: we show how to significantly improve previous algorithms for solving the approximate common divisor problem and breaking CLT13 cryptographic multilinear maps.Comment: 16 page

Revisiting Shared Data Protection Against Key Exposure

This paper puts a new light on secure data storage inside distributed systems. Specifically, it revisits computational secret sharing in a situation where the encryption key is exposed to an attacker. It comes with several contributions: First, it defines a security model for encryption schemes, where we ask for additional resilience against exposure of the encryption key. Precisely we ask for (1) indistinguishability of plaintexts under full ciphertext knowledge, (2) indistinguishability for an adversary who learns: the encryption key, plus all but one share of the ciphertext. (2) relaxes the "all-or-nothing" property to a more realistic setting, where the ciphertext is transformed into a number of shares, such that the adversary can't access one of them. (1) asks that, unless the user's key is disclosed, noone else than the user can retrieve information about the plaintext. Second, it introduces a new computationally secure encryption-then-sharing scheme, that protects the data in the previously defined attacker model. It consists in data encryption followed by a linear transformation of the ciphertext, then its fragmentation into shares, along with secret sharing of the randomness used for encryption. The computational overhead in addition to data encryption is reduced by half with respect to state of the art. Third, it provides for the first time cryptographic proofs in this context of key exposure. It emphasizes that the security of our scheme relies only on a simple cryptanalysis resilience assumption for blockciphers in public key mode: indistinguishability from random, of the sequence of diferentials of a random value. Fourth, it provides an alternative scheme relying on the more theoretical random permutation model. It consists in encrypting with sponge functions in duplex mode then, as before, secret-sharing the randomness

Batch Fully Homomorphic Encryption over the Integers

We extend the fully homomorphic encryption scheme over the integers of van Dijk et al. (DGHV) to batch fully homomorphic encryption, i.e. to a scheme that supports encrypting and homomorphically processing a vector of plaintext bits as a single ciphertext. Our variant remains semantically secure under the (error-free) approximate GCD problem. We also show how to perform arbitrary permutations on the underlying plaintext vector given the ciphertext and the public key. Our scheme offers competitive performance: we describe an implementation of the fully homomorphic evaluation of AES encryption, with an amortized cost of about 12 minutes per AES ciphertext on a standard desktop computer; this is comparable to the timings presented by Gentry et al. at Crypto 2012 for their implementation of a Ring-LWE based fully homomorphic encryption scheme

Externalized Fingerprint Matching

The 9/11 tragedy triggered an increased interest in biometric passports. According to several sources \cite{sp2}, the electronic ID market is expected to increase by more than 50\% {\sl per annum} over the three coming years, excluding China. \smallskip To cost-effectively address this foreseen explosion, a very inexpensive memory card (phonecard-like card) capable of performing fingerprint matching is paramount.\smallskip This paper presents such a solution. The proposed protocol is based on the following idea: the card stores the user\u27s fingerprint information to which random minutiae were added at enrolment time (we denote this scrambled template by $t$). The card also stores a binary string $w$ encoding which of the minutiae in $t$ actually belong to the holder. When an identification session starts, the terminal reads $t$ from the card and, based upon the incoming scanner data, determines which of the minutiae in $t$ are genuine. The terminal forms a candidate $w\u27$ and sends it to the card. All the card needs to do is test that the Hamming weight of $w \oplus w\u27$ is smaller than a security threshold $d$. \smallskip It follows that the card only needs to embark passive data storage capabilities, one exclusive-or gate, a shift register, a counter and a comparator (less than 40 logical gates)

Factoring N=prqsN=p^r q^s for Large rr and ss

International audienceBoneh et al. showed at Crypto 99 that moduli of the form N = p^r q can be factored in polynomial time when r ≃ log(p). Their algorithm is based on Coppersmith’s technique for finding small roots of polynomial equations. In this paper we show that N = p^r q^s can also be factored in polynomial time when r or s is at least (log p)^3; therefore we identify a new class of integers that can be efficiently factored.We also generalize our algorithm to moduli with k prime factors N = \prod_{i=1}^k p_i^{r_i} ; we show that a non-trivial factor of N can be extracted in polynomial-time if one of the exponents r_i is large enough

Supplemental Access Control (PACE v2): Security Analysis of PACE Integrated Mapping

We describe and analyze the password-based key establishment protocol PACE v2 Integrated Mapping (IM), an evolution of PACE v1 jointly proposed by Gemalto and Sagem Sécurité. PACE v2 IM enjoys the following properties: patent-freeness3 (to the best of current knowledge in the field); full resistance to dictionary attacks, secrecy and forward secrecy in the security model agreed upon by the CEN TC224 WG16 group; optimal performances. The PACE v2 IM protocol is intended to provide an alternative to the German PACE v1 protocol, which is also the German PACE v2 Generic Mapping (GM) protocol, proposed by the German Federal Office for Information Security (BSI). In this document, we provide a description of PACE v2 IM, a description of the security requirements one expects from a password-based key establishment protocol in order to support secure applications, and a security proof of PACE v2 IM in the so-called Bellare-Pointcheval-Rogaway (BPR) security model

New attacks on PKCS#1 v1.5 encryption

Abstract. This paper introduces two new attacks on pkcs#1 v1.5, an rsa-based encryption standard proposed by RSA Laboratories. As opposed to Bleichenbacher's attack, our attacks are chosen-plaintext only, i.e. they do not make use of a decryption oracle. The first attack applies to small public exponents and shows that a plaintext ending by sufficiently many zeroes can be recovered efficiently when two or more ciphertexts corresponding to the same plaintext are available. We believe the technique we employ to be of independent interest, as it extends Coppersmith's low-exponent attack to certain length parameters. Our second attack is applicable to arbitrary public exponents, provided that most message bits are zeroes. It seems to constitute the first chosen-plaintext attack on an rsa-based encryption standard that yields to practical results for any public exponent

High-order Polynomial Comparison and Masking Lattice-based Encryption

The main protection against side-channel attacks consists in computing every function with multiple shares via the masking countermeasure. For IND-CCA secure lattice-based encryption schemes, the masking of the decryption algorithm requires the high-order computation of a polynomial comparison. In this paper, we describe and evaluate a number of different techniques for such high-order comparison, always with a security proof in the ISW probing model. As an application, we describe the full high-order masking of the NIST standard Kyber, with a concrete implementation on ARM Cortex M architecture, and a t-test evaluation