Takeshi Nasako

A New Trapdoor in Knaspsack Public-Key Cryptosystem with Two Sequences as the Public Key

In this paper we propose a new trapdoor in knapsack public-key cryptosystem, where two independent sequences is used as the public key. We show that the proposed scheme is secure against the low-density attack, because the density can be made as large as one desires. We also discuss the security of the secret key of the proposed scheme.

Security of a Class of Knapsack Public-Key Cryptosystems against Low-Density Attack

In 2003, Kobayashi et al. proposed a new class of knapsack public-key cryptosystems over Gaussian integer ring. This scheme using two-sequences as the public key. In 2005, Sakamoto and Hayashi proposed an improved version of Kobayashis scheme. In this paper, we propose the knapsack PKC using l-sequences as the public key and present the low-density attack on it. We have described Schemes R and G for l = 2, in which the public keys are constructed over rational integer ring and over Gaussian integer ring, respectively. We discusses on the difference of the security against the low-density attack. We show that the security levels of Schemes R and G differ only slightly.

A note on performance of low-density attack for several knapsack PKCs

The order of the public-key components of knapsack cryptosystems are usually scrambled by a random permutation. It is well known that the effect of the scrambling is to keep the secret key secure. However, little is known about the influence that the scrambling affects the security against LDA in the knapsack cryptosystem. In this paper, we report the performances of LDA for the chosen permutations on several trap-doors in knapsack cryptosystems.

A Note on Security of KMN PKC

In this paper we describe the KMN PKC and the special class of it. KMN PKC has the feature that, two sequences are used as the public keys. We discuss on the security of KMN PKC against the low-density attack with computer experiments.

Relationship between weight of plaintext and successful attacks in knapsack cryptosystems

The density is a very important parameter in knapsack public-key cryptosystems. It is known that the knapsack cryptosystem is broken with the low-density attack when the density is low. In 2005, Nguyen and Stern introduced the pseudo-density instead of the conventional density in order to evaluate CR and OTU cryptosystems. In 2008, Kunihiro introduced a new density in order to unify the conventional density and the pseudo-density. From Kunihiros result, we can guess that the plaintext is disclosed with the low-density attack when the weight of the plaintext is low even in the conventional knapsack PKC. In this paper, we investigate the relationship between the weight of plaintext and successful attacks in conventional knapsack cryptosystems.

Security of Double-Sequence Knapsack PKC and Single-Sequence Knapsack PKC against Low-Density Attack

The study of the knapsack PKC is important from both practical and theoretical standpoints. We proposed a double-sequence knapsack PKC on the basis of MH PKC. We also proposed a single-sequence knapsack PKC using the Chinese remainder theorem on the basis of this scheme. In this paper, we explain the double-sequence knapsack PKC and the single-sequence knapsack PKC. We describe examples of trapdoors based on the conventional trapdoors. We evaluate the breaking rate of the double-sequence knapsack PKC and the single-sequence knapsack PKC with the low-density attack by computer experiments.

Security of Knapsack PKC with Plaintext Encoding against Low-Density Attack

Merkle and Hellman proposed the first knapsack cryptosystem. However, it was broken because the density is not sufficiently high. The knapsack scheme is expected to be one of the post quantum cryptosystems. In this paper, we describe the high-density knapsack PKCs with plaintext encoding over GF(2). We discuss the influence of the number of non-zero elements of the generator matrix on the security against the low-density attack. As the result, the scheme with plaintext encoding is secure against the low-density attack when the Hamming weight of the generator matrix is sufficiently large.

A note on security of knapsack PKC using plaintext encoding over finite fields

Merkle and Hellman proposed a knapsack cryptosystem. However, it was broken because the density is not sufficiently high. In this paper, we shall explain the high-density knapsack PKCs with plaintext encoding over GF(2). We discuss the influence of the number of non-zero elements of generator matrix on the security against the low-density attack. As the result, this scheme is secure against the low-density attack when the Hamming weight of generator matrix is sufficiently large.

Effectiveness of plaintext encoding in knapsack PKC

Knapsack public-key cryptosystem is known to be vulnerable to the low-density attack (LDA) when the density is low. Nasako and Murakami proposed the method of realizing high density by plaintext encoding over finite fields. However, little is known about the effectiveness of plaintext encoding against LDA in the knapsack cryptosystem. In this paper, we confirm that the plaintext encoding is very effective in order to be secure against LDA.