This paper describes simple and efficient (linear-preserving) reductions between the Decision Diffie-Hellman problem and related problems.

The MOV and FR algorithms, which are representative attacks on elliptic curve cryptosystems, reduce the elliptic curve discrete logarithm problem (ECDLP) to the discrete logarithm problem in a finite field. This paper studies these algorithms and introduces the following three results. First, we show an explicit condition under which the MOV algorithm can be applied to non-supersingular elliptic curves. Next, by comparing the effectiveness of the MOV algorithm to that of the FR algorithm, it is explicitly shown that the condition needed for the MOV algorithm to be subexponential is the same as that for the FR algorithm except for elliptic curves of trace two. Finally, a new explicit reduction algorithm is proposed for the ECDLP over elliptic curves of trace two. This algorithm differs from a simple realization of the FR algorithm. Furthermore, we show, by experimental results, that the running time of the proposed algorithm is shorter than that of the original FR algorithm.

Since the invention of the RSA scheme, a lot of public-key encryption and signature schemes based on the intractability of integer factoring have been proposed. Most employ integers of the form N = p q, such as the RSA scheme, but some employ integers of the form N = pr q. It has been reported that RSA decryption speed can be greatly improved by using N = pr q integers for large r. On the other hand, Boneh et al. proposed a novel integer factoring method for integers such as N = pr q for large r. This factoring algorithm, the so-called Lattice Factoring Method, is based on the LLL-algorithm. This paper proposes a new method for factoring integers of the form N = pr q for large r and gives a new characterization of r such that factoring integers N = pr q is easier. More precisely, the proposed method strongly depends on the size and smoothness of the exponent, r. The theoretical consideration of and implementation of our method presented in this paper show that if r satisfies a certain condition our method is faster than both Elliptic Curve Method and Lattice Factoring Method. In particular, the theoretical consideration in this paper mainly employs the techniques described in the excellent paper by Adleman, Pomerance and Rumely that addresses primality testing.

This paper analyzes security of sequential multiple encryptions based on asymmetric key encryptions, and shows that a sequential construction of secure multiple encryptions exists. The sequential multiple encryption scheme can be proved to be indistinguishable against chosen ciphertext attacks for multiple encryptions (IND-ME-CCA), where the adversary can access to the decryption oracle of the multiple encryption, even when all the underlying encryptions of the multiple encryption are indistinguishable against chosen plaintext attacks (IND-CPA). We provide an extended security notion of sequential multiple encryptions, in which the adversary is allowed to access decryption oracles of the underlying encryptions in addition to the multiple encryption, and show that our constructed scheme satisfies the security notion when all the underlying encryptions are indistinguishable against chosen ciphertext attacks (IND-CCA).

This paper proposes new candidate one-way functions constructed with a certain type of endomorphisms on non-supersingular elliptic curves. We can show that the one-wayness of our proposed functions is equivalent to some special cases of the co-Diffie-Hellman assumption. Also a digital signature scheme is explicitly described using our proposed functions.

In recent years, the study of the security of Elliptic Curve Cryptosystems (ECCs) have been received much attention. The MOV algorithm, which reduces the elliptic curve discrete log problem (ECDLP) to the discrete log problem in finite fields with the Weil pairing, is a representative attack on ECCs. Recently Kanayama et al. observed a realization of the MOV algorithm for non-supersingular elliptic curves under the weakest condition. Shikata et al. independently considered a realization of the MOV algorithm for non-supersingular elliptic curves and proposed a generalization of the MOV algorithm. This short note explicitly shows that, under a usual cryptographical condition, we can apply the MOV algorithm to non-supersingular elliptic curves by using the multiplication by constant maps as in the case of supersingular. Namely, it is explicitly showed that we don't need such a generalization in order to realize the MOV algorithm for non-supersingular elliptic curves under a usual cryptographical condition.

This paper provides methods for construction of pairing-based cryptosystems based on non-supersingular elliptic curves.

This paper examines similarities between the Decision Diffie-Hellman (DDH) assumption and the Quadratic Residuosity (QR) assumption. In addition, we show that many cryptographic protocols based on the QR assumption can be reconstructed using the DDH assumption.

This paper provides a sufficient condition to construct timed-release public-key encryption (TRPKE), where the constructed TRPKE scheme guarantees strong security against malicious time servers, proposed by Chow et al., and strong security against malicious receivers, defined by Cathalo et al., in the random oracle model if the component IBE scheme is IND-ID-CPA secure, the component PKE scheme is IND-ID-CPA secure, and the PKE scheme satisfies negligible γ-uniformity for every public key. Although Chow et al. proposed a strongly secure TRPKE scheme, which is concrete in the standard model, to the best of our knowledge, the proposed construction is the first generic one for TRPKE that guarantees strong security even in the random oracle model.

This paper proposes a generic construction of hierarchical identity-based identification (HIBI) protocols secure against impersonation under active and concurrent attacks in the standard model. The proposed construction converts a digital signature scheme existentially unforgeable against chosen message attacks, where the scheme has a protocol for showing possession of a signing key, not a signature. Our construction is based on the so-called certificate-based construction of hierarchical identity-based cryptosystems, and utilizes a variant of the well-known OR-proof technique to ensure the security against impersonation under active and concurrent attacks. We also present several concrete examples of our construction employing the Waters signature (EUROCRYPT 2005), and other signatures. As results, its concurrent security of each instantiation is proved under the computational Diffie-Hellman (CDH) assumption, the RSA assumption, or their variants in the standard model. Chin, Heng, and Goi proposed an HIBI protocol passively and concurrently secure under the CDH and one-more CDH assumption, respectively (FGIT-SecTech 2009). However, its security is proved in the random oracle model.