This paper proposes a bit-commitment scheme, BC(), and an efficient statistical zero-knowledge (in short, SZK) protocol in which, for any given multi-variable polynomial, f(X1,,Xt), and any given modulus, n, a prover, P, gives (I1,,It) to a verifier,ν, and can convince ν that P knows (x1,,xt) which satisfies f(x1,,xt) 0 (mod n) and Ii = BC(xi), (i = 1,,t). The proposed protocol is O(|n|) times more efficient than the corresponding previous ones. The (knowledge) soundness of our protocol holds under a computational assumption, the intractability of a modified RSA problem (see Def. 3.2), while the (statistical) zero-knowledgeness of the protocol needs no computational assumption. The protocol can be employed to construct various practical cryptographic protocols, such as fair exchange, untraceable electronic cash and verifiable secret sharing protocols.

In a seminal paper of identity based encryption (IBE), Boneh and Franklin [6] mentioned an interesting transform from an IBE scheme to a signature scheme, which was observed by Moni Naor. In this paper, we give formal security treatments for this transform and discover several implications and separations among security notions of IBE and transformed signature. For example, we show for such a successful transform, one-wayness of IBE is an essential condition. Additionally, we give a sufficient and necessary condition for converting a semantically secure IBE scheme into an existentially unforgeable signature scheme. Our results help establish strategies on design and automatic security proof of signature schemes from (possibly weak) IBE schemes. We also show some separation results which strongly support that one-wayness, rather than semantic security, of IBE captures an essential condition to achieve secure signature.

We present a simple solution to secretly sharing a factoring witness (for given N) in a publicly-verifiable manner. Compared to the previous PVSS schemes to secretly sharing a factoring witness, the scheme enjoys the following properties: (1) the formal proofs of security can be given; (2) it is designed to be conceptually simpler; (3) it needs fewer communicated bits and, if not-so low exponent RSA (e.g., e > 219+1) is used in the previous schemes, fewer computations; (4) no general multi-party computation is required in the preparation phase.

The ring signature allows a signer to leak secrets anonymously, without the risk of identity escrow. At the same time, the ring signature provides great flexibility: No group manager, no special setup, and the dynamics of group choice. The ring signature is, however, vulnerable to malicious or irresponsible signers in some applications, because of its anonymity. In this paper, we propose a traceable ring signature scheme. A traceable ring scheme is a ring signature except that it can restrict "excessive" anonymity. The traceable ring signature has a tag that consists of a list of ring members and an issue that refers to, for instance, a social affair or an election. A ring member can make any signed but anonymous opinion regarding the issue, but only once (per tag). If the member submits another signed opinion, possibly pretending to be another person who supports the first opinion, the identity of the member is immediately revealed. If the member submits the same opinion, for instance, voting "yes" regarding the same issue twice, everyone can see that these two are linked. The traceable ring signature can suit to many applications, such as an anonymous voting on a BBS. We formalize the security definitions for this primitive and show an efficient and simple construction in the random oracle model.

We propose a new security class, called plaintext simulatability, defined over the public-key encryption schemes. The notion of plaintext simulatability (denoted PS) is similar to the notion of plaintext awareness (denoted PA) defined in [3], but it is "properly" a weaker security class for public-key encryption. It is known that PA implies the class of CCA2-secure encryption (denoted IND-CCA2) but not vice versa. In most cases, PA is "unnecessarily" strong--In such cases, PA is only used to study that the public-key encryption scheme involved meets IND-CCA2, because it looks much easier to treat the membership of PA than to do "directly" the membership of IND-CCA2. We show that PS also implies IND-CCA2, while preserving such a technical advantage as well as PA. We present two novel CCA2-secure public-key encryption schemes, which should have been provided with more complicated security analyses. One is a random-oracle version of Dolev-Dwork-Naor's encryption scheme [8],[9]. Unlike the original scheme, this construction is efficient. The other is a public-key encryption scheme based on a strong pseudo-random permutation family [16] which provides the optimal ciphertext lengths for verifying the validity of ciphertexts, i.e., (ciphertext size) = (message size) + (randomness size). According to [19], such a construction remains open. Both schemes meet PS but not PA.

We study non-malleability of multiple public-key encryption (ME) schemes. The main difference of ME from the threshold public-key encryption schemes is that there is no dealer to share a secret among users; each user can independently choose their own public-keys; and a sender can encrypt a message under ad-hoc multiple public keys of his choice. In this paper we tackle non-malleability of ME. We note that the prior works only consider confidentiality of messages and treat the case that all public keys are chosen by honest users. In the multiple public-key setting, however, some application naturally requires non-malleability of ciphertexts under multiple public keys including malicious users'. Therefore, we study the case and have obtained the following results:·We present three definitions of non-malleability of ME, simulation-based, comparison-based, and indistinguishability-based ones. These definitions can be seen as an analogue of those of non-malleable public-key encryption (PKE) schemes. Interestingly, our definitions are all equivalent even for the “invalid-allowing” relations. We note that the counterparts of PKE are not equivalent for the relations.·The previous strongest security notion for ME, “indistinguishability against strong chosen-ciphertext attacks (sMCCA)” [1], does not imply our notion of non-malleability against chosen-plaintext attacks.·Non-malleability of ME guarantees that the single message indistinguishability-based notion is equivalent to the multiple-message simulation-based notion, which provides designers a fundamental benefit.·We define new, stronger decryption robustness for ME. A non-malleable ME scheme is meaningful in practice if it also has the decryption robustness.·We present a constant ciphertext-size ME scheme (meaning that the length of a ciphertext is independent of the number of public-keys) that is secure in our strongest security notion of non-malleability. Indeed, the ciphertext overhead (i.e., the length of a ciphertext minus that of a plaintext) is the combined length of two group elements plus one hash value, regardless of the number of public keys. Then, the length of the partial decryption of one user consists of only two group elements, regardless of the length of the plaintext.

Traceable ring signatures, proposed at PKC'07, are a variant of ring signatures, which allow a signer to anonymously sign a message with a tag behind a ring, i.e., a group of users chosen by the signer, unless he signs two messages with the same tag. However, if a signer signs twice on the same tag, the two signatures will be linked and the identity of the signer will be revealed when the two signed messages are different. Traceable ring signatures can be applied to anonymous write-in voting without any special voting authority and electronic coupon services. The previous traceable ring signature scheme relies on random oracles at its security and the signature size is linear in the number of ring members. This paper proposes the first secure traceable ring signature schemes without random oracles in the common reference string model. In addition, the proposed schemes have a signature size of O(), where N is the number of users in the ring.

Leakage resilient cryptography is often considered in the presence of a very strong leakage oracle: An adversary may submit arbitrary efficiently computable function f to the leakage oracle to receive f(x), where x denotes the entire secret that a party possesses. This model is somewhat too strong in the setting of public-key encryption (PKE). It is known that no secret-key leakage resilient PKE scheme exists if the adversary may have access to the secret-key leakage oracle to receive only one bit after it was given the challenge ciphertext. Similarly, there exists no sender-randomness leakage resilient PKE scheme if one-bit leakage occurs after the target public key was given to the adversary. At TCC 2011, Halevi and Lin have broken the barrier of after-the-fact leakage, by proposing the so-called split state model, where a secret key of a party is explicitly divided into at least two pieces, and the adversary may have not access to the entire secret at once, but each divided pieces, one by one. In the split-state model, they have constructed post-challenge secret-key leakage resilient CPA secure PKEs from hash proof systems, but the construction of CCA secure post-challenge secret-key leakage PKE has remained open. They have also remained open to construct sender-randomness leakage PKE in the split state model. This paper provides a solution to the open issues. We also note that the proposal of Halevi and Lin is post-challenge secret-key leakage CPA secure against a single challenge ciphertext; not against multiple challenges. We present an efficient generic construction that converts any CCA secure PKE scheme into a multiple-challenge CCA secure PKE that simultaneously tolerates post-challenge secret-key and sender-randomness leakage in the split state model, without any additional assumption. In addition, our leakage amount of the resulting schemes is the same as that of Halevi and Lin CPA PKE, i.e., (1/2+γ)l/2 where l denotes the length of the entire secret (key or randomness) and γ denotes a universal (possitive) constant less than 1/2. Our conversion is generic and available for many other public-key primitives. For instance, it can convert any identity-based encryption (IBE) scheme to a post-challenge master-key leakage and sender-randomness leakage secure IBE.

At Eurocrypt'98, Okamoto and Uchiyama presented a new trap-door (one-way) function based on factoring, while Fujisaki and Okamoto, at CRYPTO'99, showed a generic conversion from just one-way encryption to chosen-cipher secure encryption in the random oracle model. This paper shows that the result of combining both schemes is well harmonized (rather than an arbitrary combination) and, in the sense of exact security, boosts the level of security more than would be expected from [6]--The security of the scheme yielded by the combination is tightly reduced from factoring. This paper also gives a rigorous description of the new scheme, because this type of encryption may suffer serious damage if poorly implemented. The proposed scheme is at least as efficient as any other chosen-cipher secure asymmetric encryption scheme such as [2],[4],[13].

This paper presents a new non-interactive string-commitment scheme that achieves universally composable security. Security is proven under the decisional composite residuosity (DCR) assumption (or the decisional Diffie-Hellman (DDH) assumption) in the common reference string (CRS) model. The universal composability (UC) is a very strong security notion. If cryptographic protocols are proven secure in the UC framework, then they remain secure even if they are composed with arbitrary protocols and polynomially many copies of the protocols are run concurrently. Many UC commitment schemes in the CRS model have been proposed, but they are either interactive commitment or bit-commitment (not string-commitment) schemes. We note, however, that although our scheme is the first non-interactive UC string-commitment scheme, a CRS is not reusable. We use an extension of all-but-one trapdoor functions (ABO-TDFs) proposed by Peikert and Waters at STOC 2008 as an essential building block. Our main idea is to extend (original deterministic) ABO-TDFs to probabilistic ones by using the homomorphic properties of their function indices. The function indices of ABO-TDFs consist of ciphertexts of homomorphic encryption schemes (such as ElGamal, and Damgåd-Jurik encryption). Therefore we can re-randomize the output of ABO-TDFs by re-randomization of ciphertexts. This is a new application of ABO-TDFs.

We present a constant-size signature scheme under the CDH assumption. It has a tighter security reduction than any other constant-size signature scheme with a security reduction to solving some intractable search problems. Hofheinz, Jager, and Knapp (PKC 2012) presented a constant-size signature scheme under the CDH assumption with a reduction loss of O(q), where q is the number of signing queries. They also proved that the reduction loss of O(q) is optimal in a black-box security proof. To the best of our knowledge, no constant-size signature scheme has been proposed with a tighter reduction (to the hardness of a search problem) than that proposed by Hofheinz et al., even if it is not re-randomizable. We remark that our scheme is not re-randomizable. We achieve the reduction loss of O(q/d), where d is the number of group elements in a public key.

This paper proposes practical escrow cash schemes with particular emphasis on countermeasures against social crimes such as money laundering and extortion. The proposed cash schemes restrict "unconditional" privacy in order to prevent these social crimes while preserving off-line-ness, divisibility and transferability, properties listed in [25] as criteria for ideal cash schemes.

The ESIGN signature scheme was initially proposed in 1985. Since then, several variants have been proposed, but only a few have been formally supported using the methodology of provable security. In addition, these schemes are different from the ESIGN-PSS signature scheme submitted to ISO/IEC-14888-2 for standardization. It is believed that ESIGN-PSS is secure against the chosen-message attack, however, there has not yet been any report verifying this belief. This paper presents the security proofs of ESIGN-PSS and a variant of this scheme, denoted ESIGN-PSS-R, which is a signature scheme comprising the ESIGN signature mechanism and the PSS-R mechanism.

This paper presents a simple and generic conversion from a public-key encryption scheme that is indistinguishable against chosen-plaintext attacks into a public-key encryption scheme that is indistinguishable against adaptive chosen-ciphertext attacks in the random oracle model. The scheme obtained by the conversion is as efficient as the original encryption scheme and the security reduction is very tight in the exact security manner.

At Eurocrypt 2011, Lindell presented practical static and adaptively UC-secure commitment schemes based on the DDH assumption. Later, Blazy et al. (at ACNS 2013) improved the efficiency of the Lindell's commitment schemes. In this paper, we present static and adaptively UC-secure commitment schemes based on the same assumption and further improve the communication and computational complexity, as well as the size of the common reference string.

This paper presents a new non-interactive multi-trapdoor commitment scheme from the standard RSA assumption. Multi-trapdoor commitment is a stronger variant of trapdoor commitment. Its notion was introduced by Gennaro at CRYPTO 2004. Multi-trapdoor commitment schemes are very useful because we can convert a non-interactive multi-trapdoor commitment scheme into a non-interactive and reusable non-malleable commitment scheme by using one-time signature and transform any proof of knowledge into a concurrently non-malleable one (this can be used as concurrently secure identification). Gennaro gave concrete constructions of multi-trapdoor commitment, but its security relies on stronger assumptions, such as the strong RSA assumption and the q-strong Diffie-Hellman assumption as opposed to our construction based on the standard RSA assumption. As a corollary of our results, we constructed a non-interactive and reusable non-malleable commitment scheme from the standard RSA assumption. Our scheme is based on the Hohenberger-Waters (weak) signature scheme presented at CRYPTO 2009. Several non-interactive and reusable non-malleable commitment schemes (in the common reference string model) have been proposed, but they all rely on stronger assumptions (such as the strong RSA assumption). Thus, we give the first construction of a non-interactive and reusable non-malleable commitment scheme from the standard RSA assumption.