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Lattice based encryption schemes and linear code based encryption schemes have received extensive attention in recent years since they have been considered as post-quantum candidate encryption schemes. Though LLL reduction algorithm has…
RSA is one of the most popular Public Key Cryptography based algorithm mainly used for digital signatures, encryption/decryption etc. It is based on the mathematical scheme of factorization of very large integers which is a…
This paper proposes an alternative approach to formally establishing the correctness of the RSA public key cryptosystem. The methodology presented herein deviates slightly from conventional proofs found in existing literature. Specifically,…
The difficulty of factoring large integers into primes is the basis for cryptosystems such as RSA. Due to the widespread popularity of RSA, there have been many proposed attacks on the factorization problem such as side-channel attacks…
The most known of public key cryptosystem was introduced in 1978 by Rivest, Shamir and Adleman [19] and now called the RSA public key cryptosystem in their honor. Later, a few authors gave a simply extension of RSA over algebraic numbers…
This article proposes a new method to inject backdoors in RSA and other cryptographic primitives based on the Integer Factorization problem for balanced semi-primes. The method relies on mathematical congruences among the factors of the…
We study the complexity of lattice problems in a world where algorithms, reductions, and protocols can run in superpolynomial time, revisiting four foundational results: two worst-case to average-case reductions and two protocols. We also…
Side-channel attacks are an unpredictable risk factor in cryptography. Therefore, continuous observations of physical leakages are essential to minimise vulnerabilities associated with cryptographic functions. Lightweight cryptography is a…
Cryptographic standards serve two important goals: making different implementations interoperable and avoiding various known pitfalls in commonly used schemes. This chapter discusses Public-Key Cryptography Standards (PKCS) which have…
In this paper, algorithms for multivariate public key cryptography and digital signature are described. Plain messages and encrypted messages are arrays, consisting of elements from a fixed finite ring or field. The encryption and…
Lattice cryptography schemes based on the learning with errors (LWE) hardness assumption have been standardized by NIST for use as post-quantum cryptosystems, and by HomomorphicEncryption.org for encrypted compute on sensitive data. Thus,…
Lightweight cryptography is a novel diversion from conventional cryptography that targets internet-of-things (IoT) platform due to resource constraints. In comparison, it offers smaller cryptographic primitives such as shorter key sizes,…
Currently, special attention is being paid to scenarios where the interconnection of devices with heterogeneous computational and communication capabilities it is required. It is essential to integrate security services during the stages of…
Implementations of quantum key distribution as available nowadays suffer from inefficiencies due to post processing of the raw key that severely cuts down the final secure key rate. We present a simple model for the error scattering across…
Chebyshev polynomials have been recently proposed for designing public-key systems. Indeed, they enjoy some nice chaotic properties, which seem to be suitable for use in Cryptography. Moreover, they satisfy a semi-group property, which…
Modern information communications use cryptography to keep the contents of communications confidential. RSA (Rivest-Shamir-Adleman) cryptography and elliptic curve cryptography, which are public-key cryptosystems, are widely used…
Private Information Retrieval (PIR) schemes enable users to securely retrieve files from a server without disclosing the content of their queries, thereby preserving their privacy. In 2008, Melchor and Gaborit proposed a PIR scheme that…
Exploring the symmetries underlying a previously proposed encryption scheme which relies on single-qubit rotations, we derive an improved upper bound on the maximum information that an eavesdropper might extract from all the available…
Prime factorization has been a buzzing topic in the field of number theory since time unknown. However, in recent years, alternative avenues to tackle this problem are being explored by researchers because of its direct application in the…
We present a rank metric code-based encryption scheme with key and ciphertext sizes comparable to that of isogeny-based cryptography for an equivalent security level. The system also benefits from efficient encryption and decryption…