Hard isogeny problems over RSA moduli and groups with infeasible inversion

We initiate the study of computational problems on elliptic curve isogeny graphs defined over RSA moduli. We conjecture that several variants of the neighbor-search problem over these graphs are hard, and provide a comprehensive list of cryptanalytic attempts on these problems. Moreover, based on the hardness of these problems, we provide a construction of groups with infeasible inversion, where the underlying groups are the ideal class groups of imaginary quadratic orders. Recall that in a group with infeasible inversion, computing the inverse of a group element is required to be hard, while performing the group operation is easy. Motivated by the potential cryptographic application of building a directed transitive signature scheme, the search for a group with infeasible inversion was initiated in the theses of Hohenberger and Molnar (2003). Later it was also shown to provide a broadcast encryption scheme by Irrer et al. (2004). However, to date the only case of a group with infeasible inversion is implied by the much stronger primitive of self-bilinear map constructed by Yamakawa et al. (2014) based on the hardness of factoring and indistinguishability obfuscation (iO). Our construction gives a candidate without using iO.Comment: Significant revision of the article previously titled "A Candidate Group with Infeasible Inversion" (arXiv:1810.00022v1). Cleared up the constructions by giving toy examples, added "The Parallelogram Attack" (Sec 5.3.2). 54 pages, 8 figure

Learning with Errors is easy with quantum samples

Learning with Errors is one of the fundamental problems in computational learning theory and has in the last years become the cornerstone of post-quantum cryptography. In this work, we study the quantum sample complexity of Learning with Errors and show that there exists an efficient quantum learning algorithm (with polynomial sample and time complexity) for the Learning with Errors problem where the error distribution is the one used in cryptography. While our quantum learning algorithm does not break the LWE-based encryption schemes proposed in the cryptography literature, it does have some interesting implications for cryptography: first, when building an LWE-based scheme, one needs to be careful about the access to the public-key generation algorithm that is given to the adversary; second, our algorithm shows a possible way for attacking LWE-based encryption by using classical samples to approximate the quantum sample state, since then using our quantum learning algorithm would solve LWE

Pairing-based identification schemes

We propose four different identification schemes that make use of bilinear pairings, and prove their security under certain computational assumptions. Each of the schemes is more efficient and/or more secure than any known pairing-based identification scheme

Rewriting Human History and Empowering Indigenous Communities with Genome Editing Tools.

Appropriate empirical-based evidence and detailed theoretical considerations should be used for evolutionary explanations of phenotypic variation observed in the field of human population genetics (especially Indigenous populations). Investigators within the population genetics community frequently overlook the importance of these criteria when associating observed phenotypic variation with evolutionary explanations. A functional investigation of population-specific variation using cutting-edge genome editing tools has the potential to empower the population genetics community by holding "just-so" evolutionary explanations accountable. Here, we detail currently available precision genome editing tools and methods, with a particular emphasis on base editing, that can be applied to functionally investigate population-specific point mutations. We use the recent identification of thrifty mutations in the CREBRF gene as an example of the current dire need for an alliance between the fields of population genetics and genome editing

A Blind Signature Scheme using Biometric Feature Value

Blind signature has been one of the most charming research fields of public key cryptography through which authenticity, data integrity and non-repudiation can be verified. Our research is based on the blind signature schemes which are based on two hard problems – Integer factorization and discrete logarithm problems. Here biological information like finger prints, iris, retina DNA, tissue and other features whatever its kind which are unique to an individual are embedded into private key and generate cryptographic key which consists of private and public key in the public key cryptosystem. Since biological information is personal identification data, it should be positioned as a personal secret key for a system. In this schemes an attacker intends to reveal the private key knowing the public key, has to solve both the hard problems i.e. for the private key which is a part of the cryptographic key and the biological information incorporated in it. We have to generate a cryptographic key using biometric data which is called biometric cryptographic key and also using that key to put signature on a document. Then using the signature we have to verify the authenticity and integrity of the original message. The verification of the message ensures the security involved in the scheme due to use of complex mathematical equations like modular arithmetic and quadratic residue as well