Using LDGM Codes and Sparse Syndromes to Achieve Digital Signatures

In this paper, we address the problem of achieving efficient code-based digital signatures with small public keys. The solution we propose exploits sparse syndromes and randomly designed low-density generator matrix codes. Based on our evaluations, the proposed scheme is able to outperform existing solutions, permitting to achieve considerable security levels with very small public keys.Comment: 16 pages. The final publication is available at springerlink.co

Wave: A New Family of Trapdoor One-Way Preimage Sampleable Functions Based on Codes

We present here a new family of trapdoor one-way Preimage Sampleable Functions (PSF) based on codes, the Wave-PSF family. The trapdoor function is one-way under two computational assumptions: the hardness of generic decoding for high weights and the indistinguishability of generalized $(U,U+V)$-codes. Our proof follows the GPV strategy [GPV08]. By including rejection sampling, we ensure the proper distribution for the trapdoor inverse output. The domain sampling property of our family is ensured by using and proving a variant of the left-over hash lemma. We instantiate the new Wave-PSF family with ternary generalized $(U,U+V)$-codes to design a "hash-and-sign" signature scheme which achieves existential unforgeability under adaptive chosen message attacks (EUF-CMA) in the random oracle model. For 128 bits of classical security, signature sizes are in the order of 15 thousand bits, the public key size in the order of 4 megabytes, and the rejection rate is limited to one rejection every 10 to 12 signatures.Comment: arXiv admin note: text overlap with arXiv:1706.0806

Improving the Performance of the SYND Stream Cipher

International audience. In 2007, Gaborit et al. proposed the stream cipher SYND as an improvement of the pseudo random number generator due to Fischer and Stern. This work shows how to improve considerably the e ciency the SYND cipher without using the so-called regular encoding and without compromising the security of the modi ed SYND stream cipher. Our proposal, called XSYND, uses a generic state transformation which is reducible to the Regular Syndrome Decoding problem (RSD), but has better computational characteristics than the regular encoding. A rst implementation shows that XSYND runs much faster than SYND for a comparative security level (being more than three times faster for a security level of 128 bits, and more than 6 times faster for 400-bit security), though it is still only half as fast as AES in counter mode. Parallel computation may yet improve the speed of our proposal, and we leave it as future research to improve the e ciency of our implementation

Monoidic Codes in Cryptography

International audienceAt SAC 2009, Misoczki and Barreto proposed a new class of codes, which have parity-check matrices that are quasi-dyadic. A special subclass of these codes were shown to coincide with Goppa codes and those were recommended for cryptosystems based on error-correcting codes. Quasi-dyadic codes have both very compact representations and allow for efficient processing, resulting in fast cryptosystems with small key sizes. In this paper, we generalize these results and introduce quasi-monoidic codes, which retain all desirable properties of quasi-dyadic codes. We show that, as before, a subclass of our codes contains only Goppa codes or, for a slightly bigger subclass, only Generalized Srivastava codes. Unlike before, we also capture codes over fields of odd characteristic. These include wild Goppa codes that were proposed at SAC 2010 by Bernstein, Lange, and Peters for their exceptional error-correction capabilities. We show how to instantiate standard code-based encryption and signature schemes with our codes and give some preliminary parameters

LEDAcrypt: QC-LDPC Code-Based Cryptosystems with Bounded Decryption Failure Rate

We consider the QC-LDPC code-based cryptosystems named LEDAcrypt, which are under consideration by NIST for the second round of the post-quantum cryptography standardization initiative. LEDAcrypt is the result of the merger of the key encapsulation mechanism LEDAkem and the public-key cryptosystem LEDApkc, which were submitted to the first round of the same competition. We provide a detailed quantification of the quantum and classical computational efforts needed to foil the cryptographic guarantees of these systems. To this end, we take into account the best known attacks that can be mounted against them employing both classical and quantum computers, and compare their computational complexities with the ones required to break AES, coherently with the NIST requirements. Assuming the original LEDAkem and LEDApkc parameters as a reference, we introduce an algorithmic optimization procedure to design new sets of parameters for LEDAcrypt. These novel sets match the security levels in the NIST call and make the C reference implementation of the systems exhibit significantly improved figures of merit, in terms of both running times and key sizes. As a further contribution, we develop a theoretical characterization of the decryption failure rate (DFR) of LEDAcrypt cryptosystems, which allows new instances of the systems with guaranteed low DFR to be designed. Such a characterization is crucial to withstand recent attacks exploiting the reactions of the legitimate recipient upon decrypting multiple ciphertexts with the same private key, and consequentially it is able to ensure a lifecycle of the corresponding key pairs which can be sufficient for the wide majority of practical purposes

An Efficient Attack on All Concrete KKS Proposals

International audienceKabastianskii, Krouk and Smeets proposed in 1997 a digital signature scheme based on a couple of random error-correcting codes. A variation of this scheme was proposed recently and was proved to be EUF-1CMA secure in the random oracle model. In this paper we investigate the security of these schemes and suggest a simple attack based on (essentially) Stern's algorithm for finding low weight codewords. It efficiently recovers the private key of all schemes of this type existing in the literature. This is basically due to the fact that we can define a code from the available public data with unusual properties: it has many codewords whose support is concentrated in a rather small subset. In such a case, Stern's algorithm performs much better and we provide a theoretical analysis substantiating this claim. Our analysis actually shows that the insecurity of the proposed parameters is related to the fact that the rates of the couple of random codes used in the scheme were chosen to be too close. This does not compromise the security of the whole KKS scheme. It just points out that the region of weak parameters is really much larger than previously thought

Side Channel Information Set Decoding using Iterative Chunking

This paper presents an attack based on side-channel information and Information Set Decoding (ISD) on the Niederreiter cryptosystem and an evaluation of the practicality of the attack using an electromagnetic side channel. First, we describe a basic plaintext-recovery attack on the decryption algorithm of the Niederreiter cryptosystem. In case the cryptosystem is used as Key-Encapsulation Mechanism (KEM) in a key exchange, the plaintext corresponds to a session key. Our attack is an adaptation of the timing side-channel plaintext-recovery attack by Shoufan et al. from 2010 on the McEliece cryptosystem using the non-constant time Patterson’s decoding algorithm to the Niederreiter cryptosystem using the constant time Berlekamp-Massey decoding algorithm. We then enhance our attack by utilizing an ISD approach to support the basic attack and we introduce iterative column chunking to further significantly reduce the number of required side-channel measurements. We theoretically show that our attack improvements have a significant impact on reducing the number of required side-channel measurements. Our practical evaluation of the attack targets the FPGA-implementation of the Niederreiter cryptosystem in the NIST submission Classic McEliece with a constant time decoding algorithm and is feasible for all proposed parameters sets of this submission. For example, for the 256bit-security parameter set kem/mceliece6960119 we improve the basic attack that requires 5415 measurements to on average of about 560 measurements to mount a successful plaintext recovery attack. Further reductions can be achieved at increasing cost of the ISD computations

Two attacks on rank metric code-based schemes: RankSign and an IBE scheme

International audienceRankSign [29] is a code-based signature scheme proposed to the NIST competition for quantum-safe cryptography [5] and, moreover , is a fundamental building block of a new Identity-Based-Encryption (IBE) [25]. This signature scheme is based on the rank metric and enjoys remarkably small key sizes, about 10KBytes for an intended level of security of 128 bits. Unfortunately we will show that all the parameters proposed for this scheme in [5] can be broken by an algebraic attack that exploits the fact that the augmented LRPC codes used in this scheme have very low weight codewords. Therefore, without RankSign the IBE cannot be instantiated at this time. As a second contribution we will show that the problem is deeper than finding a new signature in rank-based cryptography, we also found an attack on the generic problem upon which its security reduction relies. However, contrarily to the RankSign scheme, it seems that the parameters of the IBE scheme could be chosen in order to avoid our attack. Finally, we have also shown that if one replaces the rank metric in the [25] IBE scheme by the Hamming metric, then a devastating attack can be found

Public Key Compression for Constrained Linear Signature Schemes

We formalize the notion of a constrained linear trapdoor as an abstract strategy for the generation of signature schemes, concrete instantiations of which can be found in MQ-based, code-based, and lattice-based cryptography. Moreover, we revisit and expand on a transformation by Szepieniec et al. to shrink the public key at the cost of a larger signature while reducing their combined size. This transformation can be used in a way that is provably secure in the random oracle model, and in a more aggressive variant whose security remained unproven. In this paper we show that this transformation applies to any constrained linear trapdoor signature scheme, and prove the security of the first mode in the quantum random oracle model. Moreover, we identify a property of constrained linear trapdoors that is sufficient (and necessary) for the more aggressive variant to be secure in the quantum random oracle model. We apply the transformation to an MQ-based scheme, a code-based scheme and a lattice-based scheme targeting 128-bits of post quantum security, and we show that in some cases the combined size of a signature and a public key can be reduced by more than a factor 300

Reducing the Key Size of McEliece Cryptosystem from Automorphism-induced Goppa Codes via Permutations

In this paper, we propose a new general construction to reduce the public key size of McEliece cryptosystems constructed from automorphism-induced Goppa codes. In particular, we generalize the ideas of automorphism-induced Goppa codes by considering nontrivial subsets of automorphism groups to construct Goppa codes with a nice block structure. By considering additive and multiplicative automorphism subgroups, we provide explicit constructions to demonstrate our technique. We show that our technique can be applied to automorphism-induced Goppa codes based cryptosystems to further reduce their key sizes