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Fully homomorphic encryption with relatively small key and ciphertext sizes. (English) Zbl 1281.94055
Nguyen, Phong Q. (ed.) et al., Public key cryptography – PKC 2010. 13th international conference on practice and theory in public key cryptography, Paris, France, May 26–28, 2010. Proceedings. Berlin: Springer (ISBN 978-3-642-13012-0/pbk). Lecture Notes in Computer Science 6056, 420-443 (2010).
Summary: We present a fully homomorphic encryption scheme which has both relatively small key and ciphertext size. Our construction follows that of C. Gentry [STOC 2009. New York, N.Y.: ACM, 169–178 (2009; Zbl 1257.68017)] by producing a fully homomorphic scheme from a “somewhat” homomorphic scheme. For the somewhat homomorphic scheme the public and private keys consist of two large integers (one of which is shared by both the public and private key) and the ciphertext consists of one large integer. As such, our scheme has smaller message expansion and key size than Gentry’s original scheme. In addition, our proposal allows efficient fully homomorphic encryption over any field of characteristic two.
For the entire collection see [Zbl 1188.94010].

94A60 Cryptography
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