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Efficient threshold signature, multisignature and blind signature schemes based on the Gap-Diffie-Hellman-Group signature scheme (2003)

by Alexandra Boldyreva
Venue:PROCEEDINGS OF PKC 2003, VOLUME 2567 OF LNCS
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Short signatures from the Weil pairing

by Dan Boneh, Ben Lynn, Hovav Shacham , 2001
"... We introduce a short signature scheme based on the Computational Diffie-Hellman assumption on certain elliptic and hyper-elliptic curves. The signature length is half the size of a DSA signature for a similar level of security. Our short signature scheme is designed for systems where signatures ar ..."
Abstract - Cited by 755 (25 self) - Add to MetaCart
We introduce a short signature scheme based on the Computational Diffie-Hellman assumption on certain elliptic and hyper-elliptic curves. The signature length is half the size of a DSA signature for a similar level of security. Our short signature scheme is designed for systems where signatures are typed in by a human or signatures are sent over a low-bandwidth channel.
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...res generated by dierent people on dierent messages can be aggregated into a single signature [11]. The signature also supports standard extensions such as threshold signatures and blind signatures [9=-=-=-]. Notation. We use E=F q to denote an elliptic curve y 2 = x 3 + ax + b with coecients a; b 2 F q . For r 1, we use E(F q r ) to denote the group of points on E in F q r . We use jE(F q r )j to deno...

Aggregate and Verifiably Encrypted Signatures from Bilinear Maps

by Dan Boneh, Craig Gentry, Ben Lynn, Hovav Shacham , 2002
"... An aggregate signature scheme is a digital signature that supports aggregation: Given n signatures on n distinct messages from n distinct users, it is possible to aggregate all these signatures into a single short signature. This single signature (and the n original messages) will convince the verif ..."
Abstract - Cited by 336 (12 self) - Add to MetaCart
An aggregate signature scheme is a digital signature that supports aggregation: Given n signatures on n distinct messages from n distinct users, it is possible to aggregate all these signatures into a single short signature. This single signature (and the n original messages) will convince the verifier that the n users did indeed sign the n original messages (i.e., user i signed message M i for i = 1; : : : ; n). In this paper we introduce the concept of an aggregate signature scheme, present security models for such signatures, and give several applications for aggregate signatures. We construct an efficient aggregate signature from a recent short signature scheme based on bilinear maps due to Boneh, Lynn, and Shacham. Aggregate signatures are useful for reducing the size of certificate chains (by aggregating all signatures in the chain) and for reducing message size in secure routing protocols such as SBGP. We also show that aggregate signatures give rise to verifiably encrypted signatures. Such signatures enable the verifier to test that a given ciphertext C is the encryption of a signature on a given message M . Verifiably encrypted signatures are used in contract-signing protocols. Finally, we show that similar ideas can be used to extend the short signature scheme to give simple ring signatures.
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...blem (DDH) is easy, but the Computational Diffie-Hellman problem (CDH) is hard. We refer to such groups as gap groups [6, 25]. Recently there have been a number of constructions using such gap groups =-=[6, 18, 7, 4]-=-. Surprisingly, general gap groups are insufficient for constructing efficient aggregate signatures. Instead, our construction uses a pair of groups G1; GT and a bilinear map e : G1 \ThetasG1 ! GT whe...

Toward secure key distribution in truly ad-hoc networks

by Aram Khalili, Jonathan Katz, William A. Arbaugh - in Proceedings of the International Symposium on Applications and the Internet Workshop
"... Ad-hoc networks — and in particular wireless mobile ad-hoc networks — have unique characteristics and constraints that make traditional cryptographic mechanisms and assumptions inappropriate. In particular, it may not be warranted to assume pre-existing shared secrets between members of the network ..."
Abstract - Cited by 84 (0 self) - Add to MetaCart
Ad-hoc networks — and in particular wireless mobile ad-hoc networks — have unique characteristics and constraints that make traditional cryptographic mechanisms and assumptions inappropriate. In particular, it may not be warranted to assume pre-existing shared secrets between members of the network or the presence of a common PKI. Thus, the issue of key distribution in ad-hoc networks represents an important problem. Unfortunately, this issue has been largely ignored; as an example, most protocols for secure ad-hoc routing assume that key distribution has already taken place. Traditional key distribution schemes either do not apply in an ad-hoc scenario or are not efficient enough for small, resource-constrained devices. We propose to combine efficient techniques from identity-based (ID-based) and threshold cryptography to provide a mechanism that enables flexible and efficient key distribution while respecting the constraints of ad-hoc networks. We also discuss the available mechanisms and their suitability for the proposed task. 1.
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...d Gap Diffie-Hellman (GDH) groups; i.e., groups in which the decisional Diffie-Hellman problem is efficiently computable, but the computational Diffie-Hellman problem is assumed to be hard. Boldyreva =-=[2]-=- shows that this structure can also be exploited in distributing such schemes efficiently. In particular, it allows the usual zero-knowledge interactive proofs for share verification to be replaced by...

An efficient signature scheme from bilinear pairings and its applications

by Fangguo Zhang, Reihaneh Safavi-naini, Willy Susilo - PKC 2004 , 2004
"... ... a short signature scheme (BLS scheme) using bilinear pairing on certain elliptic and hyperelliptic curves. Subsequently numerous cryptographic schemes based on BLS signature scheme were proposed. BLS short signature needs a special hash function [6, 1, 8]. This hash function is probabilistic and ..."
Abstract - Cited by 76 (12 self) - Add to MetaCart
... a short signature scheme (BLS scheme) using bilinear pairing on certain elliptic and hyperelliptic curves. Subsequently numerous cryptographic schemes based on BLS signature scheme were proposed. BLS short signature needs a special hash function [6, 1, 8]. This hash function is probabilistic and generally inefficient. In this paper, we propose a new short signature scheme from the bilinear pairings that unlike BLS, uses general cryptographic hash functions such as SHA-1 or MD5, and does not require special hash functions. Furthermore, the scheme requires less pairing operations than BLS scheme and so is more efficient than BLS scheme. We use this signature scheme to construct a ring signature scheme and a new method for delegation. We give the security proofs for the new signature scheme and the ring signature scheme in the random oracle model.

Sequential aggregate signatures and multisignatures without random oracles

by Steve Lu, Rafail Ostrovsky, Amit Sahai - In EUROCRYPT, 2006. (Cited on , 2006
"... Abstract. We present the first aggregate signature, the first multisignature, and the first verifiably encrypted signature provably secure without random oracles. Our constructions derive from a novel application of a recent signature scheme due to Waters. Signatures in our aggregate signature schem ..."
Abstract - Cited by 50 (3 self) - Add to MetaCart
Abstract. We present the first aggregate signature, the first multisignature, and the first verifiably encrypted signature provably secure without random oracles. Our constructions derive from a novel application of a recent signature scheme due to Waters. Signatures in our aggregate signature scheme are sequentially constructed, but knowledge of the order in which messages were signed is not necessary for verification. The aggregate signatures obtained are shorter than Lysyanskaya et al. sequential aggregates and can be verified more efficiently than Boneh et al. aggregates. We also consider applications to secure routing and proxy signatures. 1
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...bject – the multisignature – can take the place of n signatures by n signers, all on the same message. (Aggregate signatures can be thought of as a multisignature without this restriction.) Boldyreva =-=[6]-=- gave the first multisignature scheme in which multisignature generation does not require signer interaction, based on BLS signatures. Finally, we present the first verifiably encrypted signature sche...

Efficient Blind and Partially Blind Signatures Without Random Oracles

by Tatsuaki Okamoto , 2006
"... This paper proposes a new efficient signature scheme from bilinear maps that is secure in the standard model (i.e., without the random oracle model). Our signature scheme is more effective in many applications (e.g., blind signatures, group signatures, anonymous credentials etc.) than the existing ..."
Abstract - Cited by 48 (2 self) - Add to MetaCart
This paper proposes a new efficient signature scheme from bilinear maps that is secure in the standard model (i.e., without the random oracle model). Our signature scheme is more effective in many applications (e.g., blind signatures, group signatures, anonymous credentials etc.) than the existing secure signature schemes in the standard model. As typical applications of our signature scheme, this paper presents efficient blind signatures and partially blind signatures that are secure in the standard model. Here, partially blind signatures are a generalization of blind signatures (i.e., blind signatures are a special case of partially blind signatures) and have many applications including electronic cash and voting. Our blind signature scheme is more efficient than the existing secure blind signature schemes in the standard model such as the Camenisch-Koprowski-Warinsch [9] and Juels-Luby-Ostrovsky [24] schemes. Our partially blind signature scheme is the first one that is secure in the standard model and it is also efficient (as efficient as our blind signatures). The security proof of our blind and partially blind signature schemes requires the 2SDH assumption, a stronger variant of the SDH assumption introduced by Boneh and Boyen [7]. This paper also presents an efficient way to convert our (partially) blind signature scheme in the standard model to a scheme secure for a concurrent run of users in the common reference string (CRS) model. Finally, we present a blind signature scheme based on the Waters signature scheme.

Multi-signatures in the plain public-key model and a general forking lemma

by Mihir Bellare - In ACM CCS 06 , 2006
"... A multi-signature scheme enables a group of signers to produce a compact, joint signature on a common document, and has many potential uses. However, existing schemes impose key setup or PKI requirements that make them impractical, such as requiring a dedicated, distributed key generation protocol a ..."
Abstract - Cited by 48 (6 self) - Add to MetaCart
A multi-signature scheme enables a group of signers to produce a compact, joint signature on a common document, and has many potential uses. However, existing schemes impose key setup or PKI requirements that make them impractical, such as requiring a dedicated, distributed key generation protocol amongst potential signers, or assuming strong, concurrent zero-knowledge proofs of knowledge of secret keys done to the CA at key registration. These requirements limit the use of the schemes. We provide a new scheme that is proven secure in the plain public-key model, meaning requires nothing more than that each signer has a (certified) public key. Furthermore, the important simplification in key management achieved is not at the cost of efficiency or assurance: our scheme matches or surpasses known ones in terms of signing time, verification time and signature size, and is proven secure in the random-oracle model under a standard (not bilinear map related) assumption. The proof is based on a simplified and general Forking Lemma that may be of independent interest.
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... they might at first hearing sound far-fetched, rogue-key attacks are in fact possible to mount in practice and are a real threat. When, eventually, precise definitions [31] and proven secure schemes =-=[31, 11, 29]-=- emerged, they obviously paid a lot of attention to key setup. These schemes were, happily, proven secure against rogue-key attacks, but, unhappily, at the cost of complexity and expense in the scheme...

Unidirectional Chosen-Ciphertext Secure Proxy Re-Encryption

by Benoît Libert, Damien Vergnaud - In PKC’08, LNCS
"... Abstract. In 1998, Blaze, Bleumer and Strauss introduced a cryptographic primitive called proxy re-encryption (PRE) in which a proxy can transform – without seeing the plaintext – a ciphertext encrypted under one key into an encryption of the same plaintext under another key. The concept has recentl ..."
Abstract - Cited by 40 (1 self) - Add to MetaCart
Abstract. In 1998, Blaze, Bleumer and Strauss introduced a cryptographic primitive called proxy re-encryption (PRE) in which a proxy can transform – without seeing the plaintext – a ciphertext encrypted under one key into an encryption of the same plaintext under another key. The concept has recently drawn renewed interest. Notably, Canetti and Hohenberger showed how to properly define (and realize) chosen-ciphertext security for the primitive. Their system is bidirectional as the translation key allows converting ciphertexts in both directions. This paper presents the first unidirectional proxy re-encryption schemes with chosen-ciphertext security in the standard model (i.e. without the random oracle idealization). The first system provably fits a unidirectional extension of the Canetti-Hohenberger security model. As a second contribution, the paper considers a more realistic adversarial model where attackers may choose dishonest users ’ keys on their own. It is shown how to modify the first scheme to achieve security in the latter scenario. At a moderate expense, the resulting system provides additional useful properties such as non-interactive temporary delegations. Both constructions are efficient and rely on mild complexity assumptions in bilinear groups. Like the Canetti-Hohenberger scheme, they meet a relaxed flavor of chosen-ciphertext security introduced by Canetti, Krawczyk and Nielsen. 1
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...-encryption systems – even including passively secure or bidirectional ones [3, 19] – is that their security is analyzed in a model that implicitly makes the knowledge of secret key (KOSK) assumption =-=[12]-=- and does not capture a scenario where the generation malicious users’ public keys is left to adversaries themselves. The KOSK model is frequently used to hedge against certain harmful adversarial beh...

personal communication

by Mei Huang, Hailong Zhang, Tao Liu, Dan Tian, Lubing Gu, Muxiang Zhou, Muxiang Zhou M. D - in Proc. IEEE Int. Conference on Computer-Aided Design , 1986
"... 1 Triptolide inhibits MDM2 and induces apoptosis in acute lymphoblastic leukemia cells through a p53-independent pathway ..."
Abstract - Cited by 39 (1 self) - Add to MetaCart
1 Triptolide inhibits MDM2 and induces apoptosis in acute lymphoblastic leukemia cells through a p53-independent pathway
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... blind certificate (Mao, 1996) is a pseudonym signed by the organizer’s master key without exposing the pseudonym to the organiser. We combine the BLS (Boneh et al., 2001) and blind signature scheme (=-=Boldyreva, 2003-=-) to generate the blink certificate for a pseudonym. An AU can be verified if he possesses a valid blind certificate, that is, only the pseudonym with a verifiable certificate can be used to generate ...

Pairing-Based Cryptographic Protocols: A Survey

by Ratna Dutta, Rana Barua, Palash Sarkar
"... ..."
Abstract - Cited by 39 (0 self) - Add to MetaCart
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