# General Impossibility of Group Homomorphic Encryption in the Quantum World

@article{Armknecht2014GeneralIO, title={General Impossibility of Group Homomorphic Encryption in the Quantum World}, author={Frederik Armknecht and Tommaso Gagliardoni and Stefan Katzenbeisser and Andreas Peter}, journal={IACR Cryptol. ePrint Arch.}, year={2014}, volume={2014}, pages={29} }

Group homomorphic encryption represents one of the most important building blocks in modern cryptography. It forms the basis of widely-used, more sophisticated primitives, such as CCA2-secure encryption or secure multiparty computation. Unfortunately, recent advances in quantum computation show that many of the existing schemes completely break down once quantum computers reach maturity mainly due to Shor's algorithm. This leads to the challenge of constructing quantum-resistant group…

## 16 Citations

### Symmetric weak ternary quantum homomorphic encryption schemes

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It can be concluded that the attacker can correctly guess the encryption key with a maximum probability pk = 1/33n, thus the computational security of the users’ private quantum information can be well protected in a distributed computing environment.

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- 2019

The structure of finite commutative rings with respect to its idempotent and nilpotent elements is analyzed and a quantum-classical IND-CCA attack for ring homomorphic encryption schemes is provided.

### Sustainability of Public Key Cryptosystem in Quantum Computing Paradigm

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The aim of this chapter is to analyze the implications of quantum computing power on current public key cryptosystems and to show how these cryptsystems can be restructured to sustain in the new computing paradigm.

### Cryptanalysis of schemes based on pseudoinverse matrix

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- 2016

It is illustrated that two of the quasi-inverse based cryptography are vulnerable to a structural attack and that it only requires polynomial time to obtain the equivalent keys for some given public keys.

### On the Possibility of Classical Client Blind Quantum Computing

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This work provides an instantiation of a trapdoor (approximately) 2-regular family of functions whose security is based on the hardness of the Learning-With-Errors problem, including a first analysis of the set of usable parameters.

### Delegated Pseudo-Secret Random Qubit Generator

- Computer Science, MathematicsArXiv
- 2018

Using the functionality of delegated pseudo-secret random qubit generator (PSRQG), one could achieve for the first time a purely classical-client computational secure verifiable delegated universal quantum computing (also referred to as verifiable blind quantum computation).

### Symmetric Primitives with Structured Secrets

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This paper focuses on a special class of primitives that allow an untrusted party to transform a ciphertext encrypted under one key to a Ciphertext under another key, using some auxiliary information that does not leak the underlying data.

### Fully homomorphic encryption with applications to electronic voting

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Fully homomorphic encryption (FHE) has been dubbed the holy grail of cryptography, an elusive goal which could solve the IT world’s problems of security and trust. Research in the area exploded after…

### Fully homomorphic encryption must be fat or ugly?

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It is proved that fully homomorphic schemes are impossible for several algebraic structures, and a conjecture stating that secure FHE schemes must either have a significant ciphertext expansion or use unusual algebraic structure is proposed.

### Cryptanalysis of a cryptosystem with non-commutative platform groups

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An algebraic key-recovery attack in the polynomial computational complexity of a cryptosystem with non-commutative platform groups based on conjugator search problem is proposed.

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