On monotone formula closure of SZK

Santis, Alfredo De; Crescenzo, Giovanni Di; Persiano, Giuseppe; Yung, Moti

doi:10.1109/sfcs.1994.365745

Cited by 90 publications

(86 citation statements)

References 33 publications

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“…Our framework unifies under the theme of NIC the results of Tompa and Woll [26], De Santis, Di Crescenzo, Persiano, and Yung [25], and Itoh, Ohta, and Shizuya [16]. Actually, these works only consider the perfect setting, and focus mainly on RSR problems.…”

Section: Second Results (Informal)mentioning

confidence: 98%

“…This folklore lemma follows from [26,25], but here we provide the proof for completeness. Let us see how combining these lemmas with our characterization result yields a very useful framework.…”

Section: Second Results (Informal)mentioning

confidence: 98%

“…Our lemma on the closure of NIC under monotone boolean formulae uses the ideas of [25]. These ideas were also used in [24,27] to show closure properties.…”

Section: Second Results (Informal)mentioning

confidence: 99%

“…Our proof uses the idea behind the construction of the subroutine in the protocol of [25] (see Section 3.3 in [25]). Combining this theorem with our closure result from the next section allows us to strengthen and unify the results of [26,25,16], and achieve all the improvements claimed in the introduction. We define random self-reducibility.…”

Section: Random Self-reducibility Implies Nicmentioning

confidence: 99%

“…We use the technique of [25] to show that the class of problems possessing NIC is closed under arbitrary (as opposed to fixed) monotone boolean formulae. For perfectly hiding NIC the analysis is simple, but for statistically and computationally hiding NIC the analysis is more complicated.…”

Section: Closure Of Problems Possessing Nic Under Monotone Boolean Fomentioning

confidence: 99%

See 4 more Smart Citations

A Characterization of Non-interactive Instance-Dependent Commitment-Schemes (NIC)

Kapron

Malka

Srinivasan

Automata, Languages and Programming

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Abstract. We provide a new characterization of certain zero-knowledge protocols as non-interactive instance-dependent commitment-schemes (NIC). To obtain this result we consider the notion of V-bit protocols, which are very common, and found many applications in zero-knowledge. Our characterization result states that a protocol has a V-bit zero-knowledge protocol if and only if it has a NIC. The NIC inherits its hiding property from the zero-knowledge property of the protocol, and vice versa.Our characterization result yields a framework that strengthens and simplifies many zero-knowledge protocols in various settings. For example, applying this framework to the result of Micciancio et al. [18] (who showed that some problems, including GRAPH-NONISOMORPHISM and QUADRATIC-RESIDUOUSITY, unconditionally have a concurrent zero-knowledge proof) we easily get that arbitrary, monotone boolean formulae over a large class of problems (which contains, e.g., the complement of any random self-reducible problem) unconditionally have a concurrent zero-knowledge proof.

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Section: Second Results (Informal)mentioning

confidence: 98%

Section: Second Results (Informal)mentioning

confidence: 98%

“…Our lemma on the closure of NIC under monotone boolean formulae uses the ideas of [25]. These ideas were also used in [24,27] to show closure properties.…”

Section: Second Results (Informal)mentioning

confidence: 99%

Section: Random Self-reducibility Implies Nicmentioning

confidence: 99%

Section: Closure Of Problems Possessing Nic Under Monotone Boolean Fomentioning

confidence: 99%

See 3 more Smart Citations

A Characterization of Non-interactive Instance-Dependent Commitment-Schemes (NIC)

Kapron

Malka

Srinivasan

Automata, Languages and Programming

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Security Analysis and Fix of an Anonymous Credential System

Yang

Bao

Deng

2005

Information Security and Privacy

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A Privacy-Protecting Coupon System

Chen

Enzmann

Sadeghi

et al. 2005

Financial Cryptography and Data Security

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Abstract.A coupon represents the right to claim some service which is typically offered by vendors. In practice, issuing bundled multi-coupons is more efficient than issuing single coupons separately. The diversity of interests of the parties involved in a coupon system demands additional security properties beyond the common requirements (e.g., unforgeability). Customers wish to preserve their privacy when using the multi-coupon bundle and to prevent vendors from profiling. Vendors are interested in establishing a long-term customer relationship and not to subsidise one-time customers, since coupons are cheaper than the regular price. We propose a secure multi-coupon system that allows users to redeem a predefined number of single coupons from the same multi-coupon. The system provides unlinkability and also hides the number of remaining coupons of a multi-coupon from the vendor. A method used in the coupon system might be of independent interest. It proves knowledge of a signature on a message tuple of which a single message can be revealed while the remaining elements of the tuple, the index of the revealed message, as well as the signature remain hidden.

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On monotone formula closure of SZK

Cited by 90 publications

References 33 publications

A Characterization of Non-interactive Instance-Dependent Commitment-Schemes (NIC)

A Characterization of Non-interactive Instance-Dependent Commitment-Schemes (NIC)

Security Analysis and Fix of an Anonymous Credential System

A Privacy-Protecting Coupon System

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