Minki Song

In this paper, a blind reconstruction method of Bose-Chaudhuri-Hocquenghem (BCH) and Reed-Solomon (RS) codes is proposed, which aims to reconstruct the generator polynomials of BCH and RS codes from the intercepted noisy bitstream in non-cooperative environments.The previous blind reconstruction methods try to select correct (or noiseless) codewords or extract code information from the received bitstream. However, they need to have sufficiently correct codewords for successful reconstruction. Therefore, the existing methods are highly dependent on the channel conditions because a sufficient number of correct codewords should be available for achieving good reconstruction performance.To overcome such high dependency on channel conditions, the proposed blind reconstruction method performs error correction of single-error codewords through the proposed single-error correction method (SCM).Then, both the correct codewords and the corrected single-error codewords are utilized for blind reconstruction. Specifically, the correct codewords are selected based on the algebraic property of BCH and RS codes that codeword polynomials have consecutive roots. At the same time, the codewords presumably with a single error are selected and corrected based on the fact that the most of BCH and RS codeword polynomials with either a single error or double errors do not have consecutive roots. Based on this fact, SCM is devised, which selects and corrects the codewords with a single error with high probability. Finally, it is verified that the proposed blind reconstruction method shows much better reconstruction performance by using only one-tenth of the received codewords compared to the existing best methods even under harsh channel conditions.

In the military surveillance and security information systems, correct blind reconstruction of signal parameters from unknown signals is very important. Especially, many blind reconstruction methods of error-correcting codes have been proposed, and their theoretical performance analysis is essential for both the defender who wants to prevent information leakage and the challenger who wants to extract information from the intercepted signals. However, a proper performance analysis of most blind reconstruction methods has not been performed yet. Among many blind reconstruction methods of BCH codes proposed so far, the blind reconstruction method based on consecutive roots of generator polynomials proposed by Jo, Kwon, and Shin, called the JKS method, shows the best performance under the unknown channel information. However, the performance of the JKS method is only evaluated through simulation without performing theoretical analysis. In this paper, the JKS method is asymptotically analyzed under the binary symmetric channel with the cross-over probability $p$ . Since the blind reconstruction performance heavily depends on how many and which received codewords are used even for the same channel environment, sufficiently many codewords are assumed to perform asymptotic analysis. More specifically, an asymptotic threshold on $p$ , up to which blind reconstruction is successful, is derived when the number of received codewords is sufficiently large, which can be used as a new performance metric for blind reconstruction methods. Finally, the validity of the asymptotic analysis is confirmed through simulation.

Among many submissions to NIST post-quantum cryptography (PQC) project, NewHope is a promising key encapsulation mechanism (KEM) based on the Ring-Learning with errors (Ring-LWE) problem. Since NewHope is an indistinguishability (IND)-chosen ciphertext attack secure KEM by applying the Fujisaki-Okamoto transform to an IND-chosen plaintext attack secure public-key encryption, accurate calculation of decryption failure rate (DFR) is required to guarantee resilience against attacks that exploit decryption failures. However, the current upper bound (UB) on DFR of NewHope is rather loose because the compression noise, the effect of encoding/decoding of NewHope, and the approximation effect of centered binomial distribution are not fully considered. Furthermore, since NewHope is a Ring-LWE based cryptography, there is a problem of error dependency among error coefficients, which makes accurate DFR calculation difficult. In this paper, we derive much tighter UB on DFR than the current UB by using constraint relaxation and union bound. Especially, the above-mentioned factors are all considered in the derivation of new UB and the centered binomial distribution is not approximated. Since the error dependency is also considered, the new UB is much closer to the real DFR than the current UB. Furthermore, the new UB is parameterized by using Chernoff-Cramer bound to facilitate the calculation of new UB for the parameters of NewHope. Since the new UB is much lower than the DFR requirement of PQC, this DFR margin can be used to improve NewHope. As a result, the security level and bandwidth efficiency of NewHope are improved by 7.2 % and 5.9 %, respectively.

Lattice-based cryptography is one of the most promising schemes for post-quantum cryptography. Among the many lattice-based cryptosystems, FrodoKEM is a well-known key-encapsulation mechanism (KEM) based on (plain) learning with errors (LWE) problems and is advantageous in that the hardness is based on the problem of unstructured lattices. There are many cryptosystems that adopt errorcorrecting codes (ECCs) to improve performance, such as LAC, ThreeBears, and Round5. However, for lattice-based cryptosystems that do not use ring structures such as FrodoKEM, it is difficult to use ECCs because the number of transmitted symbols is small. In this study, we propose a method to apply ECCs and Gray codes to FrodoKEM by encoding the bits converted from the encrypted symbols. It is shown that the proposed method improves the security level and/or the bandwidth of FrodoKEM, and 192 message bits, 50% more than the original 128 bits, can be transmitted using one of the modified Frodo-640’s.