On a New, Efficient Framework for Falsifiable Non-interactive Zero-Knowledge Arguments

Et kunnskapsløst bevis er en protokoll mellom en bevisfører og en attestant. Bevisføreren har som mål å overbevise attestanten om at visse utsagn er korrekte, som besittelse av kortnummeret til et gyldig kredittkort, uten å avsløre noen private opplysninger, som for eksempel kortnummeret selv. I mange anvendelser er det ønskelig å bruke IIK-bevis (Ikke-interaktive kunnskapsløse bevis), der bevisføreren produserer kun en enkelt melding som kan bekreftes av mange attestanter. En ulempe er at sikre IIK-bevis for ikke-trivielle språk kun kan eksistere ved tilstedeværelsen av en pålitelig tredjepart som beregner en felles referansestreng som blir gjort tilgjengelig for både bevisføreren og attestanten. Når ingen slik part eksisterer liter man av og til på ikke-interaktiv vitne-uskillbarhet, en svakere form for personvern. Studiet av effektive og sikre IIK-bevis er en kritisk del av kryptografi som har blomstret opp i det siste grunnet anvendelser i blokkjeder. I den første artikkelen konstruerer vi et nytt IIK-bevis for språkene som består av alle felles nullpunkter for en endelig mengde polynomer over en endelig kropp. Vi demonstrerer nytteverdien av beviset ved flerfoldige eksempler på anvendelser. Særlig verdt å merke seg er at det er mulig å gå nesten automatisk fra en beskrivelse av et språk på et høyt nivå til definisjonen av IIK-beviset, som minsker behovet for dedikert kryptografisk ekspertise. I den andre artikkelen konstruerer vi et IIV-bevis ved å bruke en ny kompilator. Vi utforsker begrepet Kunnskapslydighet (et sterkere sikkerhetsbegrep enn lydighet) for noen konstruksjoner av IIK-bevis. I den tredje artikkelen utvider vi arbeidet fra den første artikkelen ved å konstruere et nytt IIK-bevis for mengde-medlemskap som lar oss bevise at et element ligger, eller ikke ligger, i den gitte mengden. Flere nye konstruksjoner har bedre effektivitet sammenlignet med allerede kjente konstruksjoner.A zero-knowledge proof is a protocol between a prover, and a verifier. The prover aims to convince the verifier of the truth of some statement, such as possessing credentials for a valid credit card, without revealing any private information, such as the credentials themselves. In many applications, it is desirable to use NIZKs (Non-Interactive Zero Knowledge) proofs, where the prover sends outputs only a single message that can be verified by many verifiers. As a drawback, secure NIZKs for non-trivial languages can only exist in the presence of a trusted third party that computes a common reference string and makes it available to both the prover and verifier. When no such party exists, one sometimes relies on non interactive witness indistinguishability (NIWI), a weaker notion of privacy. The study of efficient and secure NIZKs is a crucial part of cryptography that has been thriving recently due to blockchain applications. In the first paper, we construct a new NIZK for the language of common zeros of a finite set of polynomials over a finite field. We demonstrate its usefulness by giving a large number of example applications. Notably, it is possible to go from a high-level language description to the definition of the NIZK almost automatically, lessening the need for dedicated cryptographic expertise. In the second paper, we construct a NIWI using a new compiler. We explore the notion of Knowledge Soundness (a security notion stronger than soundness) of some NIZK constructions. In the third paper, we extended the first paper’s work by constructing a new set (non-)membership NIZK that allows us to prove that an element belongs or does not belong to the given set. Many new constructions have better efficiency compared to already-known constructions.Doktorgradsavhandlin

On Adaptive Security of Delayed-Input Sigma Protocols and Fiat-Shamir NIZKs

We study adaptive security of delayed-input Sigma protocols and non-interactive zero-knowledge (NIZK) proof systems in the common reference string (CRS) model. Our contributions are threefold: - We exhibit a generic compiler taking any delayed-input Sigma protocol and returning a delayed-input Sigma protocol satisfying adaptive-input special honest-verifier zero-knowledge (SHVZK). In case the initial Sigma protocol also satisfies adaptive-input special soundness, our compiler preserves this property. - We revisit the recent paradigm by Canetti et al. (STOC 2019) for obtaining NIZK proof systems in the CRS model via the Fiat-Shamir transform applied to so-called trapdoor Sigma protocols, in the context of adaptive security. In particular, assuming correlation-intractable hash functions for all sparse relations, we prove that Fiat- Shamir NIZKs satisfy either: (i) Adaptive soundness (and non-adaptive zero-knowledge), so long as the challenge is obtained by hashing both the prover’s first round and the instance being proven; (ii) Adaptive zero-knowledge (and non-adaptive soundness), so long as the challenge is obtained by hashing only the prover’s first round, and further assuming that the initial trapdoor Sigma protocol satisfies adaptive-input SHVZK. - We exhibit a generic compiler taking any Sigma protocol and returning a trapdoor Sigma protocol. Unfortunately, this transform does not preserve the delayed-input property of the initial Sigma protocol (if any). To complement this result, we also give yet another compiler taking any delayed-input trapdoor Sigma protocol and returning a delayed-input trapdoor Sigma protocol with adaptive-input SHVZK. An attractive feature of our first two compilers is that they allow obtaining efficient delayed-input Sigma protocols with adaptive security, and efficient Fiat-Shamir NIZKs with adaptive soundness (and non-adaptive zero-knowledge) in the CRS model. Prior to our work, the latter was only possible using generic NP reductions

Set (Non-)Membership NIZKs from Determinantal Accumulators

We construct a falsifiable set (non-)membership NIZK $\Pi^*$ that is considerably more efficient than known falsifiable set (non-)membership NIZKs. It also has a universal CRS. $\Pi^*$ is based on the novel concept of determinantal accumulators. Determinantal primitives have a similar relation to recent pairing-based (non-succinct) NIZKs of Couteau and Hartmann (Crypto 2020) and Couteau et al. (CLPØ, Asiacrypt 2021) that structure-preserving primitives have to the Groth-Sahai NIZK. We also extend CLPØ by proposing efficient (non-succinct) set non-membership arguments for a large class of languages

Algebraic Group Model with Oblivious Sampling

In the algebraic group model (AGM), an adversary has to return with each group element a linear representation with respect to input group elements. In many groups, it is easy to sample group elements obliviously without knowing such linear representations. Since the AGM does not model this, it can be used to prove the security of spurious knowledge assumptions. We show several well-known zk-SNARKs use such assumptions. We propose AGM with oblivious sampling (AGMOS), an AGM variant where the adversary can access an oracle that allows sampling group elements obliviously from some distribution. We show that AGM and AGMOS are different by studying the family of ``total knowledge-of-exponent\u27\u27 assumptions, showing that they are all secure in the AGM, but most are not secure in the AGMOS if the DL holds. We show an important separation in the case of the KZG commitment scheme. We show that many known AGM reductions go through also in the AGMOS, assuming a novel falsifiable assumption TOFR. We prove that TOFR is secure in a version of GGM with oblivious sampling

NIWI and New Notions of Extraction for Algebraic Languages

We give an efficient construction of a computational non-interactive witness indistinguishable (NIWI) proof in the plain model, and investigate notions of extraction for NIZKs for algebraic languages. Our starting point is the recent work of Couteau and Hartmann (CRYPTO 2020) who developed a new framework (CH framework) for constructing non-interactive zero-knowledge proofs and arguments under falsifiable assumptions for a large class of languages called algebraic languages. In this paper, we construct an efficient NIWI proof in the plain model for algebraic languages based on the CH framework. In the plain model, our NIWI construction is more efficient for algebraic languages than state-of-the-art Groth-Ostrovsky-Sahai (GOS) NIWI (JACM 2012). Next, we explore knowledge soundness of NIZK systems in the CH framework. We define a notion of strong f-extractability, and show that the CH proof system satisfies this notion. We then put forth a new definition of knowledge soundness called semantic extraction. We explore the relationship of semantic extraction with existing knowledge soundness definitions and show that it is a general definition that recovers black-box and non-black-box definitions as special cases. Finally, we show that NIZKs for algebraic languages in the CH framework cannot satisfy semantic extraction. We extend this impossibility to a class of NIZK arguments over algebraic languages, namely quasi-adaptive NIZK arguments that are constructed from smooth projective hash functions

Efficient NIZKs for Algebraic Sets

Significantly extending the framework of (Couteau and Hartmann, Crypto 2020), we propose a general methodology to construct NIZKs for showing that an encrypted vector $\vec{\chi}$ belongs to an algebraic set, i.e., is in the zero locus of an ideal $\mathscr{I}$ of a polynomial ring. In the case where $\mathscr{I}$ is principal, i.e., generated by a single polynomial $F$, we first construct a matrix that is a ``quasideterminantal representation\u27\u27 of $F$ and then a NIZK argument to show that $F (\vec{\chi}) = 0$. This leads to compact NIZKs for general computational structures, such as polynomial-size algebraic branching programs. We extend the framework to the case where \IDEAL is non-principal, obtaining efficient NIZKs for R1CS, arithmetic constraint satisfaction systems, and thus for $\mathsf{NP}$. As an independent result, we explicitly describe the corresponding language of ciphertexts as an algebraic language, with smaller parameters than in previous constructions that were based on the disjunction of algebraic languages. This results in an efficient GL-SPHF for algebraic branching programs

Thyroid Cancer Imaging In Vivo by Targeting the Anti-Apoptotic Molecule Galectin-3

Background The prevalence of thyroid nodules increases with age, average 4-7% for the U.S.A. adult population, but it is much higher (19-67%) when sub-clinical nodules are considered. About 90% of these lesions are benign and a reliable approach to their preoperative characterization is necessary. Unfortunately conventional thyroid scintigraphy does not allow the distinction among benign and malignant thyroid proliferations but it provides only functional information (cold or hot nodules). The expression of the anti-apoptotic molecule galectin-3 is restricted to cancer cells and this feature has potential diagnostic and therapeutic implications. We show here the possibility to obtain thyroid cancer imaging in vivo by targeting galectin-3. Methods The galectin-3 based thyroid immuno-scintigraphy uses as radiotracer a specific 99mTc-radiolabeled mAb. A position-sensitive high-resolution mini-gamma camera was used as imaging capture device. Human galectin-3 positive thyroid cancer xenografts (ARO) and galectin-3 knockout tumors were used as targets in different experiments in vivo. 38 mice with tumor mass of about 1 gm were injected in the tail vein with 100 ?Ci of 99mTc-labeled mAb to galectin-3 (30 ?g protein/in 100 ?l saline solution). Tumor images were acquired at 1 hr, 3 hrs, 6 hrs, 9 hrs and 24 hrs post injection by using the mini-gamma camera. Findings Results from different consecutive experiments show an optimal visualization of thyroid cancer xenografts between 6 and 9 hours from injection of the radiotracer. Galectin-3 negative tumors were not detected at all. At 6 hrs post-injection galectin-3 expressing tumors were correctly visualized, while the whole-body activity had essentially cleared. Conclusions These results demonstrate the possibility to distinguish preoperatively benign from malignant thyroid nodules by using a specific galectin-3 radio-immunotargeting. In vivo imaging of thyroid cancer may allow a better selection of patients referred to surgery. The possibility to apply this method for imaging and treatment of other galectin-3 expressing tumors is also discussed

Efficient NIZKs for Algebraic Sets

International audienceSignificantly extending the framework of (Couteau and Hartmann, Crypto 2020), we propose a general methodology to construct NIZKs for showing that an encrypted vector χ belongs to an algebraic set, i.e., is in the zero locus of an ideal I of a polynomial ring. In the case where I is principal, i.e., generated by a single polynomial F , we first construct a matrix that is a "quasideterminantal representation" of F and then a NIZK argument to show that F (χ) = 0. This leads to compact NIZKs for general computational structures, such as polynomial-size algebraic branching programs. We extend the framework to the case where I is non-principal, obtaining efficient NIZKs for R1CS, arithmetic constraint satisfaction systems, and thus for NP. As an independent result, we explicitly describe the corresponding language of ciphertexts as an algebraic language, with smaller parameters than in previous constructions that were based on the disjunction of algebraic languages. This results in an efficient GL-SPHF for algebraic branching programs