Performances of Cryptographic Accumulators

International audienceCryptographic accumulators are space/time efficient data structures used to verify if a value belongs to a set. They have found many applications in networking and distributed systems since their in- troduction by Benaloh and de Mare in 1993. Despite this popularity, there is currently no performance evaluation of the different existing de- signs. Symmetric and asymmetric accumulators are used likewise without any particular argument to support either of the design. We aim to es- tablish the speed of each design and their application's domains in terms of their size and the size of the values

On the Impossibility of Batch Update for Cryptographic Accumulators

A cryptographic accumulator is a scheme where a set of elements is represented by a single short value. This value, along with another value called witness allows to prove membership into the set. In their survey on accumulators [FN02], Fazzio and Nicolisi noted that the Camenisch and Lysyanskaya\u27s construction[CL02] was such that the time to update a witness after m changes to the accumulated value was proportional to m. They posed the question whether batch update was possible, namely if it was possible to build a cryptographic accumulator where the time to update witnesses is independent from the number of changes in the accumulated set. Recently, Wang et al. answered positively by giving a construction for an accumulator with batch update in [WWP07, WWP08]. In this work we show that the construction is not secure by exhibiting an attack. Moreover, we prove it cannot be fixed. If the accumulated value has been updated m times, then the time to update a witness must be at least (m) in the worst case

A new Privacy Preserving and Scalable Revocation Method for Self Sovereign Identity - The Perfect Revocation Method does not exist yet

Digital Identities are playing an essential role in our digital lives. Today, most Digital Identities are based on central architectures. Central Digital Identity providers control and know our data and thereby our Identity. Self Sovereign Identities are based on decentralized data storage and data exchange architecture, where the user is in sole control of his data and identity. Most of the issued credentials need the possibility of revocation. For a centrally managed Digital Identity system, revocation is not a problem. In decentral architectures, revocation is more challenging. Revocation can be done with different methods e.g. list based, cryptographic accumulators and with credential updates. A revocation method must be privacy preserving and must scale. This paper gives an overview of the available revocation methods, including a survey to define requirements, assess revocation groups against the requirements, highlights shortcomings of the methods and introduces a new revocation method called Linked Validity Verifiable Credentials

Performances of Cryptographic Accumulators

International audienceCryptographic accumulators are space/time efficient data structures used to verify if a value belongs to a set. They have found many applications in networking and distributed systems since their in- troduction by Benaloh and de Mare in 1993. Despite this popularity, there is currently no performance evaluation of the different existing de- signs. Symmetric and asymmetric accumulators are used likewise without any particular argument to support either of the design. We aim to es- tablish the speed of each design and their application's domains in terms of their size and the size of the values

Zero-knowledge Argument for Polynomial Evaluation with Application to Blacklists

Verification of a polynomial’s evaluation in a secret committed value plays a role in cryptographic applications such as non-membership or membership proofs. We construct a novel special honest verifier zero-knowledge argument for correct polynomial evaluation. The argument has logarithmic communication cost in the degree of the polynomial, which is a significant improvement over the state of the art with cubic root complexity at best. The argument is relatively efficient to generate and very fast to verify compared to previous work. The argument has a simple public-coin 3-move structure and only relies on the discrete logarithm assumption. The polynomial evaluation argument can be used as a building block to construct zero-knowledge membership and non-membership arguments with communication that is logarithmic in the size of the blacklist. Non-membership proofs can be used to design anonymous blacklisting schemes allowing online services to block misbehaving users without learning the identity of the user. They also allow the blocking of single users of anonymization networks without blocking the whole network

Zero-Knowledge Argument for Polynomial Evaluation with Application to Blacklists

Verification of a polynomial’s evaluation in a secret committed value plays a role in cryptographic applications such as non-membership or membership proofs. We construct a novel special honest verifier zero-knowledge argument for correct polynomial evaluation. The argument has logarithmic communication cost in the degree of the polynomial, which is a significant improvement over the state of the art with cubic root complexity at best. The argument is relatively efficient to generate and very fast to verify compared to previous work. The argument has a simple public-coin 3-move structure and only relies on the discrete logarithm assumption. The polynomial evaluation argument can be used as a building block to construct zero-knowledge membership and non-membership arguments with communication that is logarithmic in the size of the blacklist. Non-membership proofs can be used to design anonymous blacklisting schemes allowing online services to block misbehaving users without learning the identity of the user. They also allow the blocking of single users of anonymization networks without blocking the whole network

Practical zero-knowledge Protocols based on the discrete logarithm Assumption

Zero-knowledge proofs were introduced by Goldwasser, Micali, and Rackoff. A zero-knowledge proof allows a prover to demonstrate knowledge of some information, for example that they know an element which is a member of a list or which is not a member of a list, without disclosing any further information about that element. Existing constructions of zero-knowledge proofs which can be applied to all languages in NP are impractical due to their communication and computational complexity. However, it has been known since Guillou and Quisquater's identification protocol from 1988 and Schnorr's identification protocol from 1991 that practical zero-knowledge protocols for specific problems exist. Because of this, a lot of work was undertaken over the recent decades to find practical zero-knowledge proofs for various other specific problems, and in recent years many protocols were published which have improved communication and computational complexity. Nevertheless, to find more problems which have an efficient and practical zero-knowledge proof system and which can be used as building blocks for other protocols is an ongoing challenge of modern cryptography. This work addresses the challenge, and constructs zero-knowledge arguments with sublinear communication complexity, and achievable computational demands. The security of our protocols is only based on the discrete logarithm assumption. Polynomial evaluation arguments are proposed for univariate polynomials, for multivariate polynomials, and for a batch of univariate polynomials. Furthermore, the polynomial evaluation argument is applied to construct practical membership and non-membership arguments. Finally, an efficient method for proving the correctness of a shuffle is proposed. The proposed protocols have been tested against current state of the art versions in order to verify their practicality in terms of run-time and communication cost. We observe that the performance of our protocols is fast enough to be practical for medium range parameters. Furthermore, all our verifiers have a better asymptotic behavior than earlier verifiers independent of the parameter range, and in real life settings our provers perform better than provers of existing protocols. The analysis of the results shows that the communication cost of our protocols is very small; therefore, our new protocols compare very favorably to the current state of the art

Enhancing Privacy Protection:Set Membership, Range Proofs, and the Extended Access Control

Privacy has recently gained an importance beyond the field of cryptography. In that regard, the main goal behind this thesis is to enhance privacy protection. All of the necessary mathematical and cryptographic preliminaries are introduced at the start of this thesis. We then show in Part I how to improve set membership and range proofs, which are cryptographic primitives enabling better privacy protection. Part II shows how to improve the standards for Machine Readable Travel Documents (MRTDs), such as biometric passports. Regarding set membership proofs, we provide an efficient protocol based on the Boneh-Boyen signature scheme. We show that alternative signature schemes can be used and we provide a general protocol description that can be applied for any secure signature scheme. We also show that signature schemes in our design can be replaced by cryptographic accumulators. For range proofs, we provide interactive solutions where the range is divided in a base u and the u-ary digits are handled by one of our set membership proofs. A general construction is also provided for any set membership proof. We additionally explain how to handle arbitrary ranges with either two range proofs or with an improved solution based on sumset representation. These efficient solutions achieve, to date, the lowest asymptotical communication load. Furthermore, this thesis shows that the first efficient non-interactive range proof is insecure. This thesis thus provides the first efficient and secure non-interactive range proof. In the case of MRTDs, two standards exist: one produced by the International Civil Aviation Organization (ICAO) and the other by the European Union, which is called the Extended Access Control (EAC). Although this thesis focuses on the EAC, which is supposed to solve all privacy concerns, it shows that both standards fail to provide complete privacy protection. Lastly, we provide several solutions to improve them

A new dynamic accumulator for batch updates

A dynamic accumulator is an algorithm, which gathers together a large set of elements into a constant-size value such that for a given element accumulated, there is a witness confirming that the element was indeed included into the value, with a property that accumulated elements can be dynamically added and deleted into/from the original set such that the cost of an addition or deletion operation is independent of the number of accumulated elements. Although the first accumulator was presented ten years ago, there is still no standard formal definition of accumulators. In this paper, we generalize formal definitions for accumulators, formulate a security game for dynamic accumulators so-called Chosen Element Attack (CEA), and propose a new dynamic accumulator for batch updates based on the Paillier cryptosystem. Our construction makes a batch of update operations at unit cost. We prove its security under the extended strong RSA (es-RSA) assumptio