We describe a novel type of weak cryptographic private key that can exist in any discrete logarithm based public-key cryptosystem set in a group of prime order $p$ where $p-1$ has small divisors. Unlike the weak private keys based on \textit{numerical size} (such as smaller private keys, or private keys lying in an interval) that will \textit{always} exist in any DLP cryptosystems, our type of weak private keys occurs purely due to parameter choice of $p$, and hence, can be removed with appropriate value of $p$. Using the theory of implicit group representations, we present algorithms that can determine whether a key is weak, and if so, recover the private key from the corresponding public key. We analyze several elliptic curves proposed in the literature and in various standards, giving counts of the number of keys that can be broken with relatively small amounts of computation. Our results show that many of these curves, including some from standards, have a considerable number of such weak private keys. We also use our methods to show that none of the 14 outstanding Certicom Challenge problem instances are weak in our sense, up to a certain weakness bound.
Modern cryptography is essential to communication and information security for performing all kinds of security actions, such as encryption, authentication, and signature. However, the exposure possibility of keys poses a great threat to almost all modern cryptography. This article proposes a key-fusing framework, which enables a high resilience to key exposure by fusing multiple imperfect keys. The correctness of the scheme is strictly verified through a toy model that is general enough to abstract the physical-layer key generation (PLKG) mechanisms. Analysis and results demonstrate that the …
Securing a secret master key is a non-trivial task, we even argue it is impossible to fully secure it, hence we must make it as difficult as possible for any powerful adversary to steal or use the key. We introduce the reader to interesting cryptography which is starting to get more attention in terms of addressing the above problem, and we briefly overview some commercial and open-source products that can be used. Finally, we propose a set of solutions on how to secure master keys, more as guidelines rather than exact technical specifications, with aim to inspire and raise awareness of how to…
General cryptographic schemes are presented where keys can be one-time or ephemeral. Processes for key exchange are derived. Public key cryptographic schemes based on the new systems are easily established. Authentication and signature schemes are implemented. The schemes are an advance on group ring techniques and are easily implemented but highly secure. They may be integrated with error-correcting coding schemes so that encryption/coding and decryption/decoding may be done simultaneously.
Cryptocurrency wallets store the wallets private key(s), and hence, are a lucrative target for attackers. With possession of the private key, an attacker virtually owns all of the currency in the compromised wallet. Managing cryptocurrency wallets offline, in isolated ('air-gapped') computers, has been suggested in order to secure the private keys from theft. Such air-gapped wallets are often referred to as 'cold wallets.' In this paper, we show how private keys can be exfiltrated from air-gapped wallets. In the adversarial attack model, the attacker infiltrates the offline wallet, infecting i…
Ring signature is a kind of group-oriented signature. It allows a member of a group to sign messages on behalf of the group without revealing his/her identity. Certificateless public key cryptography was first introduced by Al-Riyami and Paterson in Asiacrypt 2003. In certificateless cryptography, it does not require the use of certificates to guarantee the authenticity of users' public keys. Meanwhile, certificateless cryptography does not have the key escrow problem, which seems to be inherent in the Identity-based cryptography. In this paper, we propose a concrete certificateless ring signa…
We present a key recovery attack against Y. Wang's Random Linear Code Encryption (RLCE) scheme recently submitted to the NIST call for post-quantum cryptography. This attack recovers the secret key for all the short key parameters proposed by the author.
In this paper, we have proposed a public key cryptography using recursive block matrices involving generalized Fibonacci numbers over a finite field Fp. For this, we define multinacci block matrices, a type of upper triangular matrix involving multinacci matrices at diagonal places and obtained some of its algebraic properties. Moreover, we have set up a method for key element agreement at end users, which makes the cryptography more efficient. The proposed cryptography comes with a large keyspace and its security relies on the Discrete Logarithm Problem(DLP).
In this paper we address the problem of large space consumption for protocols in the Bounded Retrieval Model (BRM), which require users to store large secret keys subject to adversarial leakage. We propose a method to derive keys for such protocols on-the-fly from weakly random private data (like text documents or photos, users keep on their disks anyway for non-cryptographic purposes) in such a way that no extra storage is needed. We prove that any leakage-resilient protocol (belonging to a certain, arguably quite broad class) when run with a key obtained this way retains a similar level of s…
Primality generation is the cornerstone of several essential cryptographic systems. The problem has been a subject of deep investigations, but there is still a substantial room for improvements. Typically, the algorithms used have two parts trial divisions aimed at eliminating numbers with small prime factors and primality tests based on an easy-to-compute statement that is valid for primes and invalid for composites. In this paper, we will showcase a technique that will eliminate the first phase of the primality testing algorithms. The computational simulations show a reduction of the primali…
Private information retrieval (PIR) is a database query protocol that provides user privacy, in that the user can learn a particular entry of the database of his interest but his query would be hidden from the data centre. Symmetric private information retrieval (SPIR) takes PIR further by additionally offering database privacy, where the user cannot learn any additional entries of the database. Unconditionally secure SPIR solutions with multiple databases are known classically, but are unrealistic because they require long shared secret keys between the parties for secure communication and sh…
The previous work showed that the Y00 protocol could stay secure with the eavesdropper's guessing probability on the secret keys being strictly less than one under an unlimitedly long known-plaintext attack with quantum memory. However, an assumption that at least a fast correlation attack is completely disabled by irregular mapping. The present study shows that the Y00 protocol can be information-theoretic secure under any quantum-computational crypto-analyses if the Y00 system is well designed. The Y00 protocol directly encrypts messages with short secret keys expanded into pseudo-random run…
The growing sophistication of cyber attacks, vulnerabilities in high computing systems and increasing dependency on cryptography to protect our digital data make it more important to keep secret keys safe and secure. Few major issues on secret keys like incorrect use of keys, inappropriate storage of keys, inadequate protection of keys, insecure movement of keys, lack of audit logging, insider threats and non-destruction of keys can compromise the whole security system dangerously. In this article, we have proposed and implemented an isolated secret key memory which can log life cycle of secre…
With the development of quantum computers, traditional cryptographic systems are facing more and more serious security threats. Fortunately, quantum key distribution (QKD) and post-quantum cryptography (PQC) are two cryptographic mechanisms with quantum-resistant security, and both will become important solutions for future information security. However, neither of them is perfect, and they are complementary. Quantum key distribution has unconditional security that post-quantum cryptography does not have, and PQC can provide secure and convenient authentication for QKD networks. In this paper,…
The evolution of quantum computers poses a serious threat to contemporary public-key encryption (PKE) schemes. To address this impending issue, the National Institute of Standards and Technology (NIST) is currently undertaking the Post-Quantum Cryptography (PQC) standardization project intending to evaluate and subsequently standardize the suitable PQC scheme(s). One such attractive approach, called Bit Flipping Key Encapsulation (BIKE), has made to the final round of the competition. Despite having some attractive features, the IND-CCA security of the BIKE depends on the average decoder failu…
University of Cambridge（剑桥大学）；Shenzhen International Center For Industrial And Applied Mathematics, Shenzhen Research Institute of Big Data（深圳国际应用数学中心，深圳大数据研究院）；Tsinghua University（清华大学）；University of California San Diego（加州大学圣地亚哥分校）
Combining Post-Quantum Cryptography and Quantum Key Distribution: Taxonomy, Constructions, Proofs, Standards, Deployments and Open Problems
College of Science and Engineering, Qatar University（卡塔尔大学科学与工程学院）；Qatar Center for Quantum Computing, College of Science and Engineering, Hamad Bin Khalifa University（哈马德·本·哈利法大学科学与工程学院量子计算中心）
