Cryptography based on the Hardness of Decoding

This thesis provides progress in the fields of for lattice and coding based cryptography. The first contribution consists of constructions of IND-CCA2 secure public key cryptosystems from both the McEliece and the low noise learning parity with noise assumption. The second contribution is a novel instantiation of the lattice-based learning with errors problem which uses uniform errors

On Massive MIMO Physical Layer Cryptosystem

In this paper, we present a zero-forcing (ZF) attack on the physical layer cryptography scheme based on massive multiple-input multiple-output (MIMO). The scheme uses singular value decomposition (SVD) precoder. We show that the eavesdropper can decrypt/decode the information data under the same condition as the legitimate receiver. We then study the advantage for decoding by the legitimate user over the eavesdropper in a generalized scheme using an arbitrary precoder at the transmitter. On the negative side, we show that if the eavesdropper uses a number of receive antennas much larger than the number of legitimate user antennas, then there is no advantage, independent of the precoding scheme employed at the transmitter. On the positive side, for the case where the adversary is limited to have the same number of antennas as legitimate users, we give an $\mathcal{O}\left(n^2\right)$ upper bound on the advantage and show that this bound can be approached using an inverse precoder.Comment: To be presented at ITW 2015, Jeju Island, South Korea. 6 Pages, 1 Figur

Cryptanalysis of a One-Time Code-Based Digital Signature Scheme

We consider a one-time digital signature scheme recently proposed by Persichetti and show that a successful key recovery attack can be mounted with limited complexity. The attack we propose exploits a single signature intercepted by the attacker, and relies on a statistical analysis performed over such a signature, followed by information set decoding. We assess the attack complexity and show that a full recovery of the secret key can be performed with a work factor that is far below the claimed security level. The efficiency of the attack is motivated by the sparsity of the signature, which leads to a significant information leakage about the secret key.Comment: 5 pages, 1 figur

A tight security reduction in the quantum random oracle model for code-based signature schemes

Quantum secure signature schemes have a lot of attention recently, in particular because of the NIST call to standardize quantum safe cryptography. However, only few signature schemes can have concrete quantum security because of technical difficulties associated with the Quantum Random Oracle Model (QROM). In this paper, we show that code-based signature schemes based on the full domain hash paradigm can behave very well in the QROM i.e. that we can have tight security reductions. We also study quantum algorithms related to the underlying code-based assumption. Finally, we apply our reduction to a concrete example: the SURF signature scheme. We provide parameters for 128 bits of quantum security in the QROM and show that the obtained parameters are competitive compared to other similar quantum secure signature schemes