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

Cloud Computing in the Quantum Era

Cloud computing has become the prominent technology of this era. Its elasticity, dynamicity, availability, heterogeneity, and pay as you go pricing model has attracted several companies to migrate their businesses' services into the cloud. This gives them more time to focus solely on their businesses and reduces the management and backup overhead leveraging the flexibility of cloud computing. On the other hand, quantum technology is developing very rapidly. Experts are expecting to get an efficient quantum computer within the next decade. This has a significant impact on several sciences including cryptography, medical research, and other fields. This paper analyses the reciprocal impact of quantum technology on cloud computing and vice versa

A lightweight McEliece cryptosystem co-processor design

Due to the rapid advances in the development of quantum computers and their susceptibility to errors, there is a renewed interest in error correction algorithms. In particular, error correcting code-based cryptosystems have reemerged as a highly desirable coding technique. This is due to the fact that most classical asymmetric cryptosystems will fail in the quantum computing era. Quantum computers can solve many of the integer factorization and discrete logarithm problems efficiently. However, code-based cryptosystems are still secure against quantum computers, since the decoding of linear codes remains as NP-hard even on these computing systems. One such cryptosystem is the McEliece code-based cryptosystem. The original McEliece code-based cryptosystem uses binary Goppa code, which is known for its good code rate and error correction capability. However, its key generation and decoding procedures have a high computation complexity. In this work we propose a design and hardware implementation of an public-key encryption and decryption co-processor based on a new variant of McEliece system. This co-processor takes the advantage of the non-binary Orthogonal Latin Square Codes to achieve much smaller computation complexity, hardware cost, and the key size.Published versio

A Lightweight McEliece Cryptosystem Co-processor Design

Due to the rapid advances in the development of quantum computers and their susceptibility to errors, there is a renewed interest in error correction algorithms. In particular, error correcting code-based cryptosystems have reemerged as a highly desirable coding technique. This is due to the fact that most classical asymmetric cryptosystems will fail in the quantum computing era. Quantum computers can solve many of the integer factorization and discrete logarithm problems efficiently. However, code-based cryptosystems are still secure against quantum computers, since the decoding of linear codes remains as NP-hard even on these computing systems. One such cryptosystem is the McEliece code-based cryptosystem. The original McEliece code-based cryptosystem uses binary Goppa code, which is known for its good code rate and error correction capability. However, its key generation and decoding procedures have a high computation complexity. In this work we propose a design and hardware implementation of an public-key encryption and decryption co-processor based on a new variant of McEliece system. This co-processor takes the advantage of the non-binary Orthogonal Latin Square Codes to achieve much smaller computation complexity, hardware cost, and the key size.Comment: 2019 Boston Area Architecture Workshop (BARC'19

Decoding Generalized Reed-Solomon Codes and Its Application to RLCE Encryption Schemes

This paper compares the efficiency of various algorithms for implementing quantum resistant public key encryption scheme RLCE on 64-bit CPUs. By optimizing various algorithms for polynomial and matrix operations over finite fields, we obtained several interesting (or even surprising) results. For example, it is well known (e.g., Moenck 1976 \cite{moenck1976practical}) that Karatsuba's algorithm outperforms classical polynomial multiplication algorithm from the degree 15 and above (practically, Karatsuba's algorithm only outperforms classical polynomial multiplication algorithm from the degree 35 and above ). Our experiments show that 64-bit optimized Karatsuba's algorithm will only outperform 64-bit optimized classical polynomial multiplication algorithm for polynomials of degree 115 and above over finite field $GF(2^{10})$. The second interesting (surprising) result shows that 64-bit optimized Chien's search algorithm ourperforms all other 64-bit optimized polynomial root finding algorithms such as BTA and FFT for polynomials of all degrees over finite field $GF(2^{10})$. The third interesting (surprising) result shows that 64-bit optimized Strassen matrix multiplication algorithm only outperforms 64-bit optimized classical matrix multiplication algorithm for matrices of dimension 750 and above over finite field $GF(2^{10})$. It should be noted that existing literatures and practices recommend Strassen matrix multiplication algorithm for matrices of dimension 40 and above. All our experiments are done on a 64-bit MacBook Pro with i7 CPU and single thread C codes. It should be noted that the reported results should be appliable to 64 or larger bits CPU architectures. For 32 or smaller bits CPUs, these results may not be applicable. The source code and library for the algorithms covered in this paper are available at http://quantumca.org/

SIGNCRYPTION ANALYZE

The aim of this paper is to provide an overview for the research that has been done so far in signcryption area. The paper also presents the extensions for the signcryption scheme and discusses the security in signcryption. The main contribution to this paper represents the implementation of the signcryption algorithm with the examples provided.ElGamal, elliptic curves, encryption, identity-based, proxy-signcryption, public key, ring-signcryption, RSA, signcryption