# Stream Ciphers: A Practical Solution for Efficient Homomorphic-Ciphertext Compression

Stream Ciphers: A Practical Solution for Efficient Homomorphic-Ciphertext Compression In typical applications of homomorphic encryption, the first step consists for Alice of encrypting some plaintext m under Bob’s public key $$\mathsf {pk}$$ pk and of sending the ciphertext $$c = \mathsf {HE}_{\mathsf {pk}}(m)$$ c = HE pk ( m ) to some third-party evaluator Charlie. This paper specifically considers that first step, i.e., the problem of transmitting c as efficiently as possible from Alice to Charlie. As others suggested before, a form of compression is achieved using hybrid encryption. Given a symmetric encryption scheme $$\mathsf {E}$$ E , Alice picks a random key k and sends a much smaller ciphertext $$c' = (\mathsf {HE}_{\mathsf {pk}}(k), \mathsf {E}_k(m))$$ c ′ = ( HE pk ( k ) , E k ( m ) ) that Charlie decompresses homomorphically into the original c using a decryption circuit $$\mathcal {C}_{{\mathsf {E}^{-1}}}$$ C E - 1 . In this paper, we revisit that paradigm in light of its concrete implementation constraints, in particular $$\mathsf {E}$$ E is chosen to be an additive IV-based stream cipher. We investigate the performances offered in this context by Trivium, which belongs to the eSTREAM portfolio, and we also propose a variant with 128-bit security: Kreyvium. We show that Trivium, whose security has been firmly established for over a decade, and the new variant Kreyvium has excellent performance. We also describe a second construction, based on exponentiation in binary fields, which is impractical but sets the lowest depth record to $$8$$ 8 for $$128$$ 128 -bit security. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Cryptology Springer Journals

# Stream Ciphers: A Practical Solution for Efficient Homomorphic-Ciphertext Compression

32 pages

/lp/springer_journal/stream-ciphers-a-practical-solution-for-efficient-homomorphic-zqg8Ifkvd4
Publisher
Springer US
Subject
Computer Science; Coding and Information Theory; Computational Mathematics and Numerical Analysis; Combinatorics; Probability Theory and Stochastic Processes; Communications Engineering, Networks
ISSN
0933-2790
eISSN
1432-1378
D.O.I.
10.1007/s00145-017-9273-9
Publisher site
See Article on Publisher Site

### Abstract

In typical applications of homomorphic encryption, the first step consists for Alice of encrypting some plaintext m under Bob’s public key $$\mathsf {pk}$$ pk and of sending the ciphertext $$c = \mathsf {HE}_{\mathsf {pk}}(m)$$ c = HE pk ( m ) to some third-party evaluator Charlie. This paper specifically considers that first step, i.e., the problem of transmitting c as efficiently as possible from Alice to Charlie. As others suggested before, a form of compression is achieved using hybrid encryption. Given a symmetric encryption scheme $$\mathsf {E}$$ E , Alice picks a random key k and sends a much smaller ciphertext $$c' = (\mathsf {HE}_{\mathsf {pk}}(k), \mathsf {E}_k(m))$$ c ′ = ( HE pk ( k ) , E k ( m ) ) that Charlie decompresses homomorphically into the original c using a decryption circuit $$\mathcal {C}_{{\mathsf {E}^{-1}}}$$ C E - 1 . In this paper, we revisit that paradigm in light of its concrete implementation constraints, in particular $$\mathsf {E}$$ E is chosen to be an additive IV-based stream cipher. We investigate the performances offered in this context by Trivium, which belongs to the eSTREAM portfolio, and we also propose a variant with 128-bit security: Kreyvium. We show that Trivium, whose security has been firmly established for over a decade, and the new variant Kreyvium has excellent performance. We also describe a second construction, based on exponentiation in binary fields, which is impractical but sets the lowest depth record to $$8$$ 8 for $$128$$ 128 -bit security.

### Journal

Journal of CryptologySpringer Journals

Published: Jan 31, 2018

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