For avoiding the exposure of plaintexts in cloud environments, some homomorphic hashing algorithms have been proposed to generate the hash value of each plaintext, and cloud environments only store the hash values and calculate the hash values for future needs. However, longer hash value generation time and longer hash value summary time may be required by these homomorphic hashing algorithms with higher security strengths. Therefore, this study proposes a homomorphic hashing based on elliptic curve cryptography (ECC) to provide a homomorphic hashing function in accordance with the characteristics of ECC. Furthermore, mathematical models and practical cases have been given to prove the proposed method. In experiments, the results show that the proposed method have higher efficiency with different security strengths.
Laboratoire d’informatique de l’École polytechnique, LIX, UMR 7161, CNRS（巴黎综合理工学院计算机实验室）；Department of Mathematics, Queens College, City University of New York（纽约市立大学皇后学院数学系）；Department of Mathematics, The City College of New York（纽约市立学院数学系）
A brief history on Homomorphic learning: A privacy-focused approach to machine learning
密码学和数据科学研究随着互联网的繁荣而呈指数级增长。传统的加密技术迫使用户在可用性、便利性和安全性之间做出权衡。加密使有价值的数据无法访问，因为每次执行任何操作都需要对其进行解密。可以节省数十亿美元，数百万人可以从加密方法中受益，这些方法不会在可用性，便利性和安全性之间妥协。同态加密就是这样一种范例，它允许对加密数据运行任意操作。它使我们能够运行任何复杂的机器学习算法，而无需访问底层原始数据。因此，同态学习提供了从由于各种政府和组织隐私规则而被忽视的敏感数据中获得见解的能力。本文追溯了Ronald L. Rivest和Len Alderman：“我们可以计算加密数据吗？”在1978年的论文中。然后，我们逐步遵循沙菲·戈德瓦瑟、克里斯汀·劳特、丹·邦奇、托马斯·桑德、唐纳德·比弗和克雷格·金特里的想法来解决这个至关重要的问题。经过30多年的集体努力，终于找到了这个重要问题的答案“是”。
Spinel: A Post-Quantum Signature Scheme Based on $\mathrm{SL}_n(\mathbb{F}_p)$ Hashing
Hassan II University（哈桑二世大学）；University of Texas, Austin（德克萨斯大学奥斯汀分校）；Queens College, City University of New York（纽约市立大学皇后学院）；Graduate Center, City University of New York（纽约市立大学研究生院）；Tandon School of Engineering, New York University（纽约大学坦登工程学院）；University of York（约克大学）
