Abstract
(Non-interactive) Trapdoor Mercurial Commitments (TMCs) were introduced by Chase et al. [8] and form a key building block for constructing zero-knowledge sets (introduced by Micali, Rabin and Kilian [28]). TMCs are quite similar and certainly imply ordinary (non-interactive) trapdoor commitments (TCs). Unlike TCs, however, they allow for some additional freedom in the way the message is opened: informally, by allowing one to claim that "if this commitment can be opened at all, then it would open to this message". Prior to this work, it was not clear if this addition is critical or not, since all the constructions of TMCs presented in [8] and [28] used strictly stronger assumptions than TCs. We give an affirmative answer to this question, by providing simple constructions of TMCs from any trapdoor bit commitment scheme. Moreover, by plugging in various trapdoor bit commitment schemes, we get, in the trusted parameters (TP) model, all the efficient constructions from [28] and [8], as well as several immediate new (either generic or efficient) constructions. In particular, we get a construction of TMCs from any one-way function in the TP model, and, by using a special flavor of TCs, called hybrid TCs [6], even in the (weaker) shared random string (SRS) model. Our results imply that (a) mercurial commitments can be viewed as surprisingly simple variations of trapdoor commitments; and (b) the existence of non-interactive zero-knowledge sets is equivalent to the existence of collision-resistant hash functions. Of independent interest, we also give a stronger and yet much simpler definition of mercurial commitments than that of [8], which is also met by our constructions in the TP model.
| Original language | English (US) |
|---|---|
| Title of host publication | Theory of Cryptography: Third Theory of Cryptography Conference, TCC 2006, Proceedings |
| Pages | 120-144 |
| Number of pages | 25 |
| Volume | 3876 LNCS |
| DOIs | |
| State | Published - 2006 |
| Event | 3rd Theory of Cryptography Conference, TCC 2006 - New York, NY, United States Duration: Mar 4 2006 → Mar 7 2006 |
Publication series
| Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
|---|---|
| Volume | 3876 LNCS |
| ISSN (Print) | 03029743 |
| ISSN (Electronic) | 16113349 |
Other
| Other | 3rd Theory of Cryptography Conference, TCC 2006 |
|---|---|
| Country | United States |
| City | New York, NY |
| Period | 3/4/06 → 3/7/06 |
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ASJC Scopus subject areas
- Computer Science(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Theoretical Computer Science
Cite this
Mercurial commitments : Minimal assumptions and efficient constructions. / Catalano, Dario; Dodis, Yevgeniy; Visconti, Ivan.
Theory of Cryptography: Third Theory of Cryptography Conference, TCC 2006, Proceedings. Vol. 3876 LNCS 2006. p. 120-144 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3876 LNCS).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Mercurial commitments
T2 - Minimal assumptions and efficient constructions
AU - Catalano, Dario
AU - Dodis, Yevgeniy
AU - Visconti, Ivan
PY - 2006
Y1 - 2006
N2 - (Non-interactive) Trapdoor Mercurial Commitments (TMCs) were introduced by Chase et al. [8] and form a key building block for constructing zero-knowledge sets (introduced by Micali, Rabin and Kilian [28]). TMCs are quite similar and certainly imply ordinary (non-interactive) trapdoor commitments (TCs). Unlike TCs, however, they allow for some additional freedom in the way the message is opened: informally, by allowing one to claim that "if this commitment can be opened at all, then it would open to this message". Prior to this work, it was not clear if this addition is critical or not, since all the constructions of TMCs presented in [8] and [28] used strictly stronger assumptions than TCs. We give an affirmative answer to this question, by providing simple constructions of TMCs from any trapdoor bit commitment scheme. Moreover, by plugging in various trapdoor bit commitment schemes, we get, in the trusted parameters (TP) model, all the efficient constructions from [28] and [8], as well as several immediate new (either generic or efficient) constructions. In particular, we get a construction of TMCs from any one-way function in the TP model, and, by using a special flavor of TCs, called hybrid TCs [6], even in the (weaker) shared random string (SRS) model. Our results imply that (a) mercurial commitments can be viewed as surprisingly simple variations of trapdoor commitments; and (b) the existence of non-interactive zero-knowledge sets is equivalent to the existence of collision-resistant hash functions. Of independent interest, we also give a stronger and yet much simpler definition of mercurial commitments than that of [8], which is also met by our constructions in the TP model.
AB - (Non-interactive) Trapdoor Mercurial Commitments (TMCs) were introduced by Chase et al. [8] and form a key building block for constructing zero-knowledge sets (introduced by Micali, Rabin and Kilian [28]). TMCs are quite similar and certainly imply ordinary (non-interactive) trapdoor commitments (TCs). Unlike TCs, however, they allow for some additional freedom in the way the message is opened: informally, by allowing one to claim that "if this commitment can be opened at all, then it would open to this message". Prior to this work, it was not clear if this addition is critical or not, since all the constructions of TMCs presented in [8] and [28] used strictly stronger assumptions than TCs. We give an affirmative answer to this question, by providing simple constructions of TMCs from any trapdoor bit commitment scheme. Moreover, by plugging in various trapdoor bit commitment schemes, we get, in the trusted parameters (TP) model, all the efficient constructions from [28] and [8], as well as several immediate new (either generic or efficient) constructions. In particular, we get a construction of TMCs from any one-way function in the TP model, and, by using a special flavor of TCs, called hybrid TCs [6], even in the (weaker) shared random string (SRS) model. Our results imply that (a) mercurial commitments can be viewed as surprisingly simple variations of trapdoor commitments; and (b) the existence of non-interactive zero-knowledge sets is equivalent to the existence of collision-resistant hash functions. Of independent interest, we also give a stronger and yet much simpler definition of mercurial commitments than that of [8], which is also met by our constructions in the TP model.
UR - http://www.scopus.com/inward/record.url?scp=33745523137&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33745523137&partnerID=8YFLogxK
U2 - 10.1007/11681878_7
DO - 10.1007/11681878_7
M3 - Conference contribution
SN - 3540327312
SN - 9783540327318
VL - 3876 LNCS
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 120
EP - 144
BT - Theory of Cryptography: Third Theory of Cryptography Conference, TCC 2006, Proceedings
ER -