Cryptographic Pairings Based on Elliptic Nets

In 2007, Stange proposed a novel method of computing the Tate pairing on an elliptic curve over a finite field. This method is based on elliptic nets, which are maps from $\mathbb{Z}^n$ to a ring that satisfy a certain recurrence relation. In this paper, we explicitly give formulae for computing some variants of the Tate pairing: Ate, Ate$_i$, R-Ate and Optimal pairings, based on elliptic nets. We also discuss their efficiency by using some experimental results

An Improvment of the Elliptic Net Algorithm

In this paper we propose a modified Elliptic Net algorithm to compute pairings. By reducing the number of the intermediate variables which should be updated in the iteration loop of the Elliptic Net algorithm, we speed up the computation of pairings. Experimental results show that the proposed method is about $14\%$ faster than the original Elliptic Net algorithm on certain supersingular elliptic curves with embedding degree $two$

Theory and Practice of Cryptography and Network Security Protocols and Technologies

In an age of explosive worldwide growth of electronic data storage and communications, effective protection of information has become a critical requirement. When used in coordination with other tools for ensuring information security, cryptography in all of its applications, including data confidentiality, data integrity, and user authentication, is a most powerful tool for protecting information. This book presents a collection of research work in the field of cryptography. It discusses some of the critical challenges that are being faced by the current computing world and also describes some mechanisms to defend against these challenges. It is a valuable source of knowledge for researchers, engineers, graduate and doctoral students working in the field of cryptography. It will also be useful for faculty members of graduate schools and universities

Certificate Transparency with Enhancements and Short Proofs

Browsers can detect malicious websites that are provisioned with forged or fake TLS/SSL certificates. However, they are not so good at detecting malicious websites if they are provisioned with mistakenly issued certificates or certificates that have been issued by a compromised certificate authority. Google proposed certificate transparency which is an open framework to monitor and audit certificates in real time. Thereafter, a few other certificate transparency schemes have been proposed which can even handle revocation. All currently known constructions use Merkle hash trees and have proof size logarithmic in the number of certificates/domain owners. We present a new certificate transparency scheme with short (constant size) proofs. Our construction makes use of dynamic bilinear-map accumulators. The scheme has many desirable properties like efficient revocation, low verification cost and update costs comparable to the existing schemes. We provide proofs of security and evaluate the performance of our scheme.Comment: A preliminary version of the paper was published in ACISP 201

Certificate Transparency with Enhancements and Short Proofs

Browsers can detect malicious websites that are provisioned with forged or fake TLS/SSL certificates. However, they are not so good at detecting malicious websites if they are provisioned with mistakenly issued certificates or certificates that have been issued by a compromised certificate authority. Google proposed certificate transparency which is an open framework to monitor and audit certificates in real time. Thereafter, a few other certificate transparency schemes have been proposed which can even handle revocation. All currently known constructions use Merkle hash trees and have proof size logarithmic in the number of certificates/domain owners. We present a new certificate transparency scheme with short (constant size) proofs. Our construction makes use of dynamic bilinear-map accumulators. The scheme has many desirable properties like efficient revocation, low verification cost and update costs comparable to the existing schemes. We provide proofs of security and evaluate the performance of our scheme.Comment: A preliminary version of the paper was published in ACISP 201

Introducing Accountability to Anonymity Networks

Many anonymous communication (AC) networks rely on routing traffic through proxy nodes to obfuscate the originator of the traffic. Without an accountability mechanism, exit proxy nodes risk sanctions by law enforcement if users commit illegal actions through the AC network. We present BackRef, a generic mechanism for AC networks that provides practical repudiation for the proxy nodes by tracing back the selected outbound traffic to the predecessor node (but not in the forward direction) through a cryptographically verifiable chain. It also provides an option for full (or partial) traceability back to the entry node or even to the corresponding user when all intermediate nodes are cooperating. Moreover, to maintain a good balance between anonymity and accountability, the protocol incorporates whitelist directories at exit proxy nodes. BackRef offers improved deployability over the related work, and introduces a novel concept of pseudonymous signatures that may be of independent interest. We exemplify the utility of BackRef by integrating it into the onion routing (OR) protocol, and examine its deployability by considering several system-level aspects. We also present the security definitions for the BackRef system (namely, anonymity, backward traceability, no forward traceability, and no false accusation) and conduct a formal security analysis of the OR protocol with BackRef using ProVerif, an automated cryptographic protocol verifier, establishing the aforementioned security properties against a strong adversarial model

Efficient software implementation of elliptic curves and bilinear pairings

Orientador: Júlio César Lopez HernándezTese (doutorado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: O advento da criptografia assimétrica ou de chave pública possibilitou a aplicação de criptografia em novos cenários, como assinaturas digitais e comércio eletrônico, tornando-a componente vital para o fornecimento de confidencialidade e autenticação em meios de comunicação. Dentre os métodos mais eficientes de criptografia assimétrica, a criptografia de curvas elípticas destaca-se pelos baixos requisitos de armazenamento para chaves e custo computacional para execução. A descoberta relativamente recente da criptografia baseada em emparelhamentos bilineares sobre curvas elípticas permitiu ainda sua flexibilização e a construção de sistemas criptográficos com propriedades inovadoras, como sistemas baseados em identidades e suas variantes. Porém, o custo computacional de criptossistemas baseados em emparelhamentos ainda permanece significativamente maior do que os assimétricos tradicionais, representando um obstáculo para sua adoção, especialmente em dispositivos com recursos limitados. As contribuições deste trabalho objetivam aprimorar o desempenho de criptossistemas baseados em curvas elípticas e emparelhamentos bilineares e consistem em: (i) implementação eficiente de corpos binários em arquiteturas embutidas de 8 bits (microcontroladores presentes em sensores sem fio); (ii) formulação eficiente de aritmética em corpos binários para conjuntos vetoriais de arquiteturas de 64 bits e famílias mais recentes de processadores desktop dotadas de suporte nativo à multiplicação em corpos binários; (iii) técnicas para implementação serial e paralela de curvas elípticas binárias e emparelhamentos bilineares simétricos e assimétricos definidos sobre corpos primos ou binários. Estas contribuições permitiram obter significativos ganhos de desempenho e, conseqüentemente, uma série de recordes de velocidade para o cálculo de diversos algoritmos criptográficos relevantes em arquiteturas modernas que vão de sistemas embarcados de 8 bits a processadores com 8 coresAbstract: The development of asymmetric or public key cryptography made possible new applications of cryptography such as digital signatures and electronic commerce. Cryptography is now a vital component for providing confidentiality and authentication in communication infra-structures. Elliptic Curve Cryptography is among the most efficient public-key methods because of its low storage and computational requirements. The relatively recent advent of Pairing-Based Cryptography allowed the further construction of flexible and innovative cryptographic solutions like Identity-Based Cryptography and variants. However, the computational cost of pairing-based cryptosystems remains significantly higher than traditional public key cryptosystems and thus an important obstacle for adoption, specially in resource-constrained devices. The main contributions of this work aim to improve the performance of curve-based cryptosystems, consisting of: (i) efficient implementation of binary fields in 8-bit microcontrollers embedded in sensor network nodes; (ii) efficient formulation of binary field arithmetic in terms of vector instructions present in 64-bit architectures, and on the recently-introduced native support for binary field multiplication in the latest Intel microarchitecture families; (iii) techniques for serial and parallel implementation of binary elliptic curves and symmetric and asymmetric pairings defined over prime and binary fields. These contributions produced important performance improvements and, consequently, several speed records for computing relevant cryptographic algorithms in modern computer architectures ranging from embedded 8-bit microcontrollers to 8-core processorsDoutoradoCiência da ComputaçãoDoutor em Ciência da Computaçã

Practical Certificateless Aggregate Signatures From Bilinear Maps

Aggregate signature is a digital signature with a striking property that anyone can aggregate n individual signatures on n different messages which are signed by n distinct signers, into a single compact signature to reduce computational and storage costs. In this work, two practical certificateless aggregate signature schemes are proposed from bilinear maps. The first scheme CAS-1 reduces the costs of communication and signer-side computation but trades off the storage, while CAS-2 minimizes the storage but sacrifices the communication costs. One can choose either of the schemes by consideration of the application requirement. Compare with ID-based schemes, our schemes do not entail public key certificates as well and achieve the trust level 3, which imply the frauds of the authority are detectable. Both of the schemes are proven secure in the random oracle model by assuming the intractability of the computational Diffie-Hellman problem over the groups with bilinear maps, where the forking lemma technique is avoided

Formalizing Soundness Proofs of SNARKs

Succinct Non-interactive Arguments of Knowledge (SNARKs) have seen interest and development from the cryptographic community over recent years, and there are now constructions with very small proof size designed to work well in practice. A SNARK protocol can only be widely accepted as secure, however, if a rigorous proof of its security properties has been vetted by the community. Even then, it is sometimes the case that these security proofs are flawed, and it is then necessary for further research to identify these flaws and correct the record. To increase the rigor of these proofs, we turn to formal methods. Focusing on the soundness aspect of a widespread class of SNARKs, we formalize proofs for six different constructions, including the well-known Groth \u2716. Our codebase is written in the Lean 3 theorem proving language, and uses a variety of techniques to simplify and automate these proofs as much as possible

Proactively Accountable Anonymous Messaging in Verdict

Among anonymity systems, DC-nets have long held attraction for their resistance to traffic analysis attacks, but practical implementations remain vulnerable to internal disruption or “jamming” attacks, which require time-consuming detection procedures to resolve. We present Verdict, the first practical anonymous group communication system built using proactively verifiable DC-nets: participants use public-key cryptography to construct DC-net ciphertexts, and use zero-knowledge proofs of knowledge to detect and exclude misbehavior before disruption. We compare three alternative constructions for verifiable DC-nets: one using bilinear maps and two based on simpler ElGamal encryption. While verifiable DC-nets incur higher computational overheads due to the public-key cryptography involved, our experiments suggest that Verdict is practical for anonymous group messaging or microblogging applications, supporting groups of 100 clients at 1 second per round or 1000 clients at 10 seconds per round. Furthermore, we show how existing symmetric-key DC-nets can “fall back” to a verifiable DC-net to quickly identify misbehavior, speeding up previous detections schemes by two orders of magnitude