Related papers: On homomorphic encryption using abelian groups: Cl…
This article proposes a comprehensive approach to implementing encryption schemes based on the automorphism group of the Hermitian function field. We utilize a three-parameter group with logarithmic representations outside the group's…
We develop a public key cryptosystem based on invariants of diagonalizable groups and investigate properties of such cryptosystem first over finite fields, then over number fields and finally over finite rings. We consider the security of…
The development of large quantum computers will have dire consequences for cryptography. Most of the symmetric and asymmetric cryptographic algorithms are vulnerable to quantum algorithms. Grover's search algorithm gives a square root time…
Homomorphic encryption (HE) is a promising cryptographic technique for enabling secure collaborative machine learning in the cloud. However, support for homomorphic computation on ciphertexts under multiple keys is inefficient. Current…
We provide a survey on the Hidden Subgroup Problem (HSP), which plays an important role in studying the security of public-key cryptosystems. We first review the abelian case, where Kitaev's algorithm yields an efficient quantum solution to…
Cryptography and data science research grew exponential with the internet boom. Legacy encryption techniques force users to make a trade-off between usability, convenience, and security. Encryption makes valuable data inaccessible, as it…
Homomorphic encryption aims at allowing computations on encrypted data without decryption other than that of the final result. This could provide an elegant solution to the issue of privacy preservation in data-based applications, such as…
Homomorphic encryption is a sophisticated encryption technique that allows computations on encrypted data to be done without the requirement for decryption. This trait makes homomorphic encryption appropriate for safe computation in…
We construct three public key knapsack cryptosystems. Standard knapsack cryptosystems hide easy instances of the knapsack problem and have been broken. The systems considered in the article face this problem: They hide a random (possibly…
Hash functions are a basic cryptographic primitive. Certain hash functions try to prove security against collision and preimage attacks by reductions to known hard problems. These hash functions usually have some additional properties that…
Homomorphic encryption is a very useful gradient protection technique used in privacy preserving federated learning. However, existing encrypted federated learning systems need a trusted third party to generate and distribute key pairs to…
The learning parity with noise (LPN) problem is a well-established computational challenge whose difficulty is critical to the security of several post-quantum cryptographic primitives such as HQC and Classic McEliece. Classically, the…
Encryption schemes often derive their power from the properties of the underlying algebra on the symbols used. Inspired by group theoretic tools, we use the centralizer of a subgroup of operations to present a private-key quantum…
This paper addresses the design of a dedicated homophonic coding for a class of communication systems which, in order to provide both reliability and security, first encode the data before encrypting it, which is referred to as the…
We propose a new homomorphic encryption scheme based on the hardness of decoding under independent random noise from certain affine families of codes. Unlike in previous lattice-based homomorphic encryption schemes, where the message is…
Fully homomorphic encryption is an encryption method with the property that any computation on the plaintext can be performed by a party having access to the ciphertext only. Here, we formally define and give schemes for quantum homomorphic…
After some excitement generated by recently suggested public key exchange protocols due to Anshel-Anshel-Goldfeld and Ko-Lee et al., it is a prevalent opinion now that the conjugacy search problem is unlikely to provide sufficient level of…
Homomorphic quantum error correction aims to protect quantum data against both unauthorized access and environmental noise during server-based processing. We investigate the algebraic compatibility between quantum homomorphic encryption and…
A fully homomorphic encryption system hides data from unauthorized parties, while still allowing them to perform computations on the encrypted data. Aside from the straightforward benefit of allowing users to delegate computations to a more…
We present novel homomorphic encryption schemes for integer arithmetic, intended for use in secure single-party computation in the cloud. These schemes are capable of securely computing only low degree polynomials homomorphically, but this…