Quantum Attacks on Modern Cryptography and Post-Quantum Cryptosystems

Cryptography is a critical technology in the modern computing industry, but the security of many cryptosystems relies on the difficulty of mathematical problems such as integer factorization and discrete logarithms. Large quantum computers can solve these problems efficiently, enabling the effective cryptanalysis of many common cryptosystems using such algorithms as Shor’s and Grover’s. If data integrity and security are to be preserved in the future, the algorithms that are vulnerable to quantum cryptanalytic techniques must be phased out in favor of quantum-proof cryptosystems. While quantum computer technology is still developing and is not yet capable of breaking commercial encryption, these steps can be taken immediately to ensure that the impending development of large quantum computers does not compromise sensitive data

A Framework for Efficient Adaptively Secure Composable Oblivious Transfer in the ROM

Oblivious Transfer (OT) is a fundamental cryptographic protocol that finds a number of applications, in particular, as an essential building block for two-party and multi-party computation. We construct a round-optimal (2 rounds) universally composable (UC) protocol for oblivious transfer secure against active adaptive adversaries from any OW-CPA secure public-key encryption scheme with certain properties in the random oracle model (ROM). In terms of computation, our protocol only requires the generation of a public/secret-key pair, two encryption operations and one decryption operation, apart from a few calls to the random oracle. In~terms of communication, our protocol only requires the transfer of one public-key, two ciphertexts, and three binary strings of roughly the same size as the message. Next, we show how to instantiate our construction under the low noise LPN, McEliece, QC-MDPC, LWE, and CDH assumptions. Our instantiations based on the low noise LPN, McEliece, and QC-MDPC assumptions are the first UC-secure OT protocols based on coding assumptions to achieve: 1) adaptive security, 2) optimal round complexity, 3) low communication and computational complexities. Previous results in this setting only achieved static security and used costly cut-and-choose techniques.Our instantiation based on CDH achieves adaptive security at the small cost of communicating only two more group elements as compared to the gap-DH based Simplest OT protocol of Chou and Orlandi (Latincrypt 15), which only achieves static security in the ROM

Separable and anonymous identity-based key issuing

In identity-based (ID-based) cryptosystems, a local registration authority (LRA) is responsible for authentication of users while the key generation center (KGC) is responsible for computing and sending the private keys to users and therefore, a secure channel is required. For privacy-oriented applications, it is important to keep in secret whether the private key corresponding to a certain identity has been requested. All of the existing ID-based key issuing schemes have not addressed this anonymity issue. Besides, the separation of duties of LRA and KGC has not been discussed as well. We propose a novel separable and anonymous ID-based key issuing scheme without secure channel. Our protocol supports the separation of duties between LRA and KGC. The private key computed by the KGC can be sent to the user in an encrypted form such that only the legitimate key requester authenticated by LRA can decrypt it, and any eavesdropper cannot know the identity corresponding to the secret key. © 2005 IEEE.published_or_final_versio

Still Wrong Use of Pairings in Cryptography

Several pairing-based cryptographic protocols are recently proposed with a wide variety of new novel applications including the ones in emerging technologies like cloud computing, internet of things (IoT), e-health systems and wearable technologies. There have been however a wide range of incorrect use of these primitives. The paper of Galbraith, Paterson, and Smart (2006) pointed out most of the issues related to the incorrect use of pairing-based cryptography. However, we noticed that some recently proposed applications still do not use these primitives correctly. This leads to unrealizable, insecure or too inefficient designs of pairing-based protocols. We observed that one reason is not being aware of the recent advancements on solving the discrete logarithm problems in some groups. The main purpose of this article is to give an understandable, informative, and the most up-to-date criteria for the correct use of pairing-based cryptography. We thereby deliberately avoid most of the technical details and rather give special emphasis on the importance of the correct use of bilinear maps by realizing secure cryptographic protocols. We list a collection of some recent papers having wrong security assumptions or realizability/efficiency issues. Finally, we give a compact and an up-to-date recipe of the correct use of pairings.Comment: 25 page

Identity-Based Cryptosystem Based on Tate Pairing

Tate Pairings on Elliptic curve Cryptography are important because they can be used to build efficient Identity-Based Cryptosystems, as well as their implementation essentially determines the efficiency of cryptosystems. In this work, we propose an identity-based encryption based on Tate Pairing on an elliptic curve. The scheme was chosen cipher text security in the random oracle model assuming a variant of computational problem Diff Hellman. This paper provides precise definitions to encryption schemes based on identity, it studies the construction of the underlying ground field, their extension to enhance the finite field arithmetic and presents a technique to accelerate the time feeding in Tate pairing algorithm

Identity-Based Cryptosystem Based on Tate Pairing

Tate Pairings on Elliptic curve Cryptography are important because they can be used to build efficient Identity-Based Cryptosystems as well as their implementation essentially determines the efficiency of cryptosystems In this work we propose an identity-based encryption based on Tate Pairing on an elliptic curve The scheme was chosen ciphertext security in the random oracle model assuming a variant of computational problem Diffie-Hellman This paper provides precise definitions to encryption schemes based on identity it studies the construction of the underlying ground field their extension to enhance the finite field arithmetic and presents a technique to accelerate the time feeding in Tate pairing algorith

Contributions to secret sharing and other distributed cryptosystems

The present thesis deals with primitives related to the eld of distributed cryptography. First, we study signcryption schemes, which provide at the same time the functionalities of encryption and signature, where the unsigncryption operation is distributed. We consider this primitive from a theoretical point of view and set a security framework for it. Then, we present two signcryption schemes with threshold unsigncryption, with di erent properties. Furthermore, we use their authenticity property to apply them in the development of a di erent primitive: digital signatures with distributed veri cation. The second block of the thesis deals with the primitive of multi-secret sharing schemes. After stating some e ciency limitations of multi-secret sharing schemes in an information-theoretic scenario, we present several multi-secret sharing schemes with provable computational security. Finally, we use the results in multi-secret sharing schemes to generalize the traditional framework of distributed cryptography (with a single policy of authorized subsets) into a multipolicy setting, and we present both a multi-policy distributed decryption scheme and a multi-policy distributed signature scheme. Additionally, we give a short outlook on how to apply the presented multi-secret sharing schemes in the design of other multi-policy cryptosystems, like the signcryption schemes considered in this thesis. For all the schemes proposed throughout the thesis, we follow the same formal structure. After de ning the protocols of the primitive and the corresponding security model, we propose the new scheme and formally prove its security, by showing a reduction to some computationally hard mathematical problem.Avui en dia les persones estan implicades cada dia més en diferents activitats digitals tant en la seva vida professional com en el seu temps lliure. Molts articles de paper, com diners i tiquets, estan sent reemplaçats més i més per objectes digitals. La criptografia juga un paper crucial en aquesta transformació, perquè proporciona seguretat en la comunicació entre els diferents participants que utilitzen un canal digital. Depenent de la situació específica, alguns requisits de seguretat en la comunicació poden incloure privacitat (o confidencialitat), autenticitat, integritat o no-repudi. En algunes situacions, repartir l'operació secreta entre un grup de participants fa el procés més segur i fiable que quan la informació secreta està centralitzada en un únic participant; la criptografia distribuïda és l’àrea de la criptografia que estudia aquestes situacions. Aquesta tesi tracta de primitives relacionades amb el camp de la criptografia distribuïda. Primer, estudiem esquemes “signcryption”, que ofereixen a la vegada les funcionalitats de xifrat i signatura, on l'operació de “unsigncryption” està distribuïda. Considerem aquesta primitiva des d’un punt de vista teòric i establim un marc de seguretat per ella. Llavors, presentem dos esquemes “signcryption” amb operació de “unsigncryption” determinada per una estructura llindar, cada un amb diferents propietats. A més, utilitzem la seva propietat d’autenticitat per desenvolupar una nova primitiva: signatures digitals amb verificació distribuïda. El segon bloc de la tesi tracta la primitiva dels esquemes de compartició de multi-secrets. Després de demostrar algunes limitacions en l’eficiència dels esquemes de compartició de multi-secrets en un escenari de teoria de la informació, presentem diversos esquemes de compartició de multi-secrets amb seguretat computacional demostrable. Finalment, utilitzem els resultats obtinguts en els esquemes de compartició de multi-secrets per generalitzar el paradigma tradicional de la criptografia distribuïda (amb una única política de subconjunts autoritzats) a un marc multi-política, i presentem un esquema de desxifrat distribuït amb multi-política i un esquema de signatura distribuïda amb multi-política. A més, donem indicacions de com es poden aplicar els nostres esquemes de compartició de multi-secrets en el disseny d’altres criptosistemes amb multi-política, com per exemple els esquemes “signcryption” considerats en aquesta tesi. Per tots els esquemes proposats al llarg d’aquesta tesi, seguim la mateixa estructura formal. Després de definir els protocols de la primitiva primitius i el model de seguretat corresponent, proposem el nou esquema i demostrem formalment la seva seguretat, mitjançant una reducció a algun problema matemàtic computacionalment difícil

ID-based Ring Signature and Proxy Ring Signature Schemes from Bilinear Pairings

In 2001, Rivest et al. firstly introduced the concept of ring signatures. A ring signature is a simplified group signature without any manager. It protects the anonymity of a signer. The first scheme proposed by Rivest et al. was based on RSA cryptosystem and certificate based public key setting. The first ring signature scheme based on DLP was proposed by Abe, Ohkubo, and Suzuki. Their scheme is also based on the general certificate-based public key setting too. In 2002, Zhang and Kim proposed a new ID-based ring signature scheme using pairings. Later Lin and Wu proposed a more efficient ID-based ring signature scheme. Both these schemes have some inconsistency in computational aspect. In this paper we propose a new ID-based ring signature scheme and a proxy ring signature scheme. Both the schemes are more efficient than existing one. These schemes also take care of the inconsistencies in above two schemes.Comment: Published with ePrint Archiv