Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/non-Hamiltonian.In this paper a computational complexity theory of the “knowledge” contained in a proof is developed. Zero-knowledge proofs are defined as those proofs that convey no additional knowledge other than the correctness of the proposition in question. Examples of zero-knowledge proof systems are given for the languages of quadratic residuosity and 'quadratic nonresiduosity. These are the first examples of zero-knowledge proofs for languages not known to be efficiently recognizable.

/pdf/the-knowledge-complexity-of-interactive-proof-systems-31apre0ecf.pdf

The knowledge complexity of interactive proof-systems

We introduce and formalize the notion of Verifiable Computation, which enables a computationally weak client to "outsource" the computation of a function F on various dynamically-chosen inputs x1, ...,xk to one or more workers. The workers return the result of the function evaluation, e.g., yi = F(xi), as well as a proof that the computation of F was carried out correctly on the given value xi. The primary constraint is that the verification of the proof should require substantially less computational effort than computing F(i) from scratch.

We present a protocol that allows the worker to return a computationally-sound, non-interactive proof that can be verified in O(mċpoly(λ)) time, where m is the bit-length of the output of F, and λ is a security parameter. The protocol requires a one-time pre-processing stage by the client which takes O(|C|ċpoly(λ)) time, where C is the smallest known Boolean circuit computing F. Unlike previous work in this area, our scheme also provides (at no additional cost) input and output privacy for the client, meaning that the workers do not learn any information about the xi or yi values.

https://link.springer.com/content/pdf/10.1007%2F978-3-642-14623-7_25.pdf

Non-interactive verifiable computing: outsourcing computation to untrusted workers

Non-interactive zero-knowledge proofs and non-interactive witnessindistinguishable proofs have played a significant role in the theory of cryptography. However, lack of efficiency has prevented them from being used in practice. One of the roots of this inefficiency is that non-interactive zeroknowledge proofs have been constructed for general NP-complete languages such as Circuit Satisfiability, causing an expensive blowup in the size of the statement when reducing it to a circuit. The contribution of this paper is a general methodology for constructing very simple and efficient non-interactive zero-knowledge proofs and non-interactive witness-indistinguishable proofs that work directly for groups with a bilinear map, without needing a reduction to Circuit Satisfiability.

Groups with bilinear maps have enjoyed tremendous success in the field of cryptography in recent years and have been used to construct a plethora of protocols. This paper provides non-interactive witness-indistinguishable proofs and non-interactive zero-knowledge proofs that can be used in connection with these protocols. Our goal is to spread the use of non-interactive cryptographic proofs from mainly theoretical purposes to the large class of practical cryptographic protocols based on bilinear groups.

/pdf/efficient-non-interactive-proof-systems-for-bilinear-groups-15qe6dsu1d.pdf

Efficient non-interactive proof systems for bilinear groups

Attribute based encryption (ABE) [13] determines decryption ability based on a user's attributes. In a multi-authority ABE scheme, multiple attribute-authorities monitor different sets of attributes and issue corresponding decryption keys to users, and encryptors can require that a user obtain keys for appropriate attributes from each authority before decrypting a message. Chase [5] gave a multi-authority ABE scheme using the concepts of a trusted central authority (CA) and global identifiers (GID). However, the CA in that construction has the power to decrypt every ciphertext, which seems somehow contradictory to the original goal of distributing control over many potentially untrusted authorities. Moreover, in that construction, the use of a consistent GID allowed the authorities to combine their information to build a full profile with all of a user's attributes, which unnecessarily compromises the privacy of the user. In this paper, we propose a solution which removes the trusted central authority, and protects the users' privacy by preventing the authorities from pooling their information on particular users, thus making ABE more usable in practice.

/pdf/improving-privacy-and-security-in-multi-authority-attribute-5699iydgrg.pdf

Improving privacy and security in multi-authority attribute-based encryption

An argument system for NP is a proof system that allows efficient verification of NP statements, given proofs produced by an untrusted yet computationally-bounded prover. Such a system is non-interactive and publicly-verifiable if, after a trusted party publishes a proving key and a verification key, anyone can use the proving key to generate non-interactive proofs for adaptively-chosen NP statements, and proofs can be verified by anyone by using the verification key.

/pdf/snarks-for-c-verifying-program-executions-succinctly-and-in-5gpviqjs3v.pdf

SNARKs for C : verifying program executions succinctly and in zero knowledge

We construct an efficient delegatable anonymous credentials system. Users can anonymously and unlinkably obtain credentials from any authority, delegate their credentials to other users, and prove possession of a credential L levels away from a given authority. The size of the proof (and time to compute it) is O(Lk), where k is the security parameter. The only other construction of delegatable anonymous credentials (Chase and Lysyanskaya, Crypto 2006) relies on general non-interactive proofs for NP-complete languages of size k ?(2 L ). We revise the entire approach to constructing anonymous credentials and identify randomizable zero-knowledge proof of knowledge systems as the key building block. We formally define the notion of randomizable non-interactive zero-knowledge proofs, and give the first instance of controlled rerandomization of non-interactive zero-knowledge proofs by a third-party. Our construction uses Groth-Sahai proofs (Eurocrypt 2008).

https://lirias.kuleuven.be/bitstream/123456789/244787/2/article-1239.pdf

Randomizable Proofs and Delegatable Anonymous Credentials

In this paper, we introduce P-signatures. A P-signature scheme consists of a signature scheme, a commitment scheme, and (1) an interactive protocol for obtaining a signature on a committed value; (2) a non-interactive proof system for proving that the contents of a commitment has been signed; (3) a noninteractive proof system for proving that a pair of commitments are commitments to the same value. We give a definition of security for P-signatures and show how they can be realized under appropriate assumptions about groups with a bilinear map. We make extensive use of the powerful suite of non-interactive proof techniques due to Groth and Sahai. Our P-signatures enable, for the first time, the design of a practical non-interactive anonymous credential system whose security does not rely on the random oracle model. In addition, they may serve as a useful building block for other privacy-preserving authentication mechanisms.

/pdf/p-signatures-and-noninteractive-anonymous-credentials-3363zjoy72.pdf

P-signatures and noninteractive anonymous credentials

/pdf/randomizable-proofs-and-delegatable-anonymous-credentials-1w3syda3ld.pdf

We describe different strategies a central authority, the boss, can use to distribute computation to untrusted contractors. Our problem is inspired by volunteer distributed computing projects such as SETI@home, which outsource computation to large numbers of participants. For many tasks, verifying a task's output requires as much work as computing it again; additionally, some tasks may produce certain outputs with greater probability than others. A selfish contractor may try to exploit these factors, by submitting potentially incorrect results and claiming a reward. Further, malicious contractors may respond incorrectly, to cause direct harm or to create additional overhead for result-checking.We consider the scenario where there is a credit system whereby users can be rewarded for good work and fined for cheating. We show how to set rewards and fines that incentivize proper behavior from rational contractors, and mitigate the damage caused by malicious contractors. We analyze two strategies: random double-checking by the boss, and hiring multiple contractors to perform the same job.We also present a bounty mechanism when multiple contractors are employed; the key insight is to give a reward to a contractor who catches another worker cheating. Furthermore, if we can assume that at least a small fraction h of the contractors are honest (1% - 10%), then we can provide graceful degradation for the accuracy of the system and the work the boss has to perform. This is much better than the Byzantine approach, which typically assumes h > 60%.

/pdf/incentivizing-outsourced-computation-1nmk1wtqyu.pdf

Incentivizing outsourced computation

We initiate a provable-security treatment of cryptographic agility. A primitive (for example PRFs, authenticated encryption schemes or digital signatures) is agile when multiple, individually secure schemes can securely share the same key. We provide a surprising connection between two seemingly unrelated but challenging questions. The first, new to this paper, is whether wPRFs (weak-PRFs) are agile. The second, already posed several times in the literature, is whether every secure (IND-R) encryption scheme is secure when encrypting cycles. We resolve the second question in the negative and thereby the first as well. We go on to provide a comprehensive treatment of agility, with definitions for various different primitives. We explain the practical motivations for agility. We provide foundational results that show to what extent it is achievable and practical constructions to achieve it to the best extent possible. On the theoretical side our work uncovers new notions and relations and settles stated open questions, and on the practical side it serves to guide developers.

/pdf/cryptographic-agility-and-its-relation-to-circular-57mwj7g5oo.pdf

Mira Belenkiy

Papers

Randomizable Proofs and Delegatable Anonymous Credentials

P-signatures and noninteractive anonymous credentials

Randomizable Proofs and Delegatable Anonymous Credentials

Incentivizing outsourced computation

Cryptographic agility and its relation to circular encryption