TY - CHAP
T1 - On Homomorphic Encryption Using Abelian Groups
T2 - Classical Security Analysis
AU - Agathocleous, Eleni
AU - Anupindi, Vishnupriya
AU - Bachmayr, Annette
AU - Martindale, Chloe
AU - Njah Nchiwo, Rahinatou Yuh
AU - Stanojkovski, Mima
PY - 2024/8/8
Y1 - 2024/8/8
N2 - Leonardi and Ruiz-Lopez recently proposed an additively homomorphic public key encryption scheme based on combining group homomorphisms with noise. Choosing parameters for their primitive requires choosing three groups G, H, and K. In their paper, Leonardi and Ruiz-Lopez claim that when G, H, and K are abelian, then their public key cryptosystem is not quantum secure. In this chapter, we study security for finite abelian groups G, H, and K in the classical case. Moreover, we study quantum attacks on instantiations with solvable groups.
AB - Leonardi and Ruiz-Lopez recently proposed an additively homomorphic public key encryption scheme based on combining group homomorphisms with noise. Choosing parameters for their primitive requires choosing three groups G, H, and K. In their paper, Leonardi and Ruiz-Lopez claim that when G, H, and K are abelian, then their public key cryptosystem is not quantum secure. In this chapter, we study security for finite abelian groups G, H, and K in the classical case. Moreover, we study quantum attacks on instantiations with solvable groups.
U2 - 10.1007/978-3-031-52163-8_1
DO - 10.1007/978-3-031-52163-8_1
M3 - Chapter in a book
SN - 978-3-031-52165-2
SN - 978-3-031-52162-1
VL - 4
T3 - Association for Women in Mathematics Series
SP - 1
EP - 27
BT - Women in Numbers Europe IV
A2 - Abdellatif, Ramla
A2 - Karemaker, Valentijn
A2 - Smajlovic, Lejla
PB - Springer
ER -