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

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

Analysis of code-based digital signature schemes

Digital signatures are in high demand because they allow authentication and non-repudiation. Existing digital signature systems, such as digital signature algorithm (DSA), elliptic curve digital signature algorithm (ECDSA), and others, are based on number theory problems such as discrete logarithmic problems and integer factorization problems. These recently used digital signatures are not secure with quantum computers. To protect against quantum computer attacks, many researchers propose digital signature schemes based on error-correcting codes such as linear, Goppa, polar, and so on. We studied 16 distinct papers based on various error-correcting codes and analyzed their various features such as signing and verification efficiency, signature size, public key size, and security against multiple attacks

The problem with the SURF scheme

There is a serious problem with one of the assumptions made in the security proof of the SURF scheme. This problem turns out to be easy in the regime of parameters needed for the SURF scheme to work. We give afterwards the old version of the paper for the reader's convenience.Comment: Warning : we found a serious problem in the security proof of the SURF scheme. We explain this problem here and give the old version of the paper afterward

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

A Post-Quantum Digital Signature Scheme from QC-LDPC Codes

We propose a novel post-quantum code-based digital signature algorithm whose security is based on the difficulty of decoding Quasi-Cyclic codes in systematic form, and whose trapdoor relies on the knowledge of a hidden Quasi-Cyclic Low-Density-Parity-Check (QC-LDPC) code. The utilization of Quasi-Cyclic (QC) codes allows us to balance between security and key size, while the LDPC property lighten the encoding complexity, thus the signing algorithm complexity, significantly

Evaluation of Code-based Signature Schemes

Code-based cryptographic schemes recently raised to prominence as quantum-safe alternatives to the currently employed number-theoretic constructions, which do not resist quantum attacks. In this article, we discuss the Courtois-Finiasz-Sendrier signature scheme and derive code-based signature schemes using the Fiat-Shamir transformation from code-based zero-knowledge identification schemes, namely the Stern scheme, the Jain-Krenn-Pietrzak-Tentes scheme, and the Cayrel-Veron-El Yousfi scheme. We analyze the security of these code-based signature schemes and derive the security parameters to achieve the 80-bit and 128-bit level of classical security. To derive the secure parameters, we have studied the hardness of Syndrome Decoding Problem. Furthermore, we implement the signature schemes, based on the Fiat-Shamir transform, which were mentioned above, and compare their performance on a PC

An Encryption Scheme based on Random Split of St-Gen Codes

Staircase-Generator codes (St-Gen codes) have recently been introduced in the design of code-based public key schemes and for the design of steganographic matrix embedding schemes. In this paper we propose a method for random splitting of St-Gen Codes and use it to design a new coding based public key encryption scheme. The scheme uses the known list decoding method for St-Gen codes, but introduces a novelty in the creation of the public and private key. We modify the classical approach for hiding the structure of the generator matrix by introducing a technique for splitting it into random parts. This approach counters the weaknesses found in the previous constructions of public key schemes using St-Gen codes. Our initial software implementation shows that encryption using Random Split of St-Gen Codes compared to original St-Gen Codes is slower by a linear factor in the number of random splits of the St-Gen code, while the decryption complexity remains the same