Cryptology ePrint Archive: Report 2002/135

Folklore, Practice and Theory of Robust Combiners

Amir Herzberg

Abstract: Cryptographic schemes are often designed as a combination of multiple component cryptographic modules. Such a combiner design is {\em robust} for a (security) specification if it meets the specification, provided that a sufficient subset of the components meet their specifications. A folklore combiner for encryption is {\em cascade}, i.e. $c={\cal E}''_{e''}({\cal E}'_{e'}(m))$. We show that cascade is a robust combiner for cryptosystems, under three important indistinguishability specifications: chosen plaintext attack (IND-CPA), non-adaptive chosen ciphertext attack (IND-CCA1), and replayable chosen ciphertext attack (IND-rCCA). We also show that cascade is not robust for the important specifications adaptive CCA (IND-CCA2) and generalized CCA (IND-gCCA). The IND-rCCA and IND-gCCA specifications are closely related, and this is an interesting difference between them. All specifications are defined within.

We also analyze few other basic and folklore combiners. In particular, we show that the following are robust combiners: the {\em parallel combiner} $f(x)=f''(x)||f'(x)$ for one-way functions , the {\em XOR-Input combiner} $c=\left({\cal E}''_{e''}(m\oplus r),{\cal E}'_{e'}(r)\right)$ for cryptosystems, and the {\em copy combiner} $f_{k'',k'}(m)=f''_{k''}(m)||f'_{k'}(m)$ for integrity tasks such as Message Authentication Codes (MAC) and signature schemes. Cascade is also robust for the hiding property of commitment schemes, and the copy combiner is robust for the binding property, but neither is a robust combiner for both properties.

We present (new) robust combiners for commitment schemes; these new combiners can be viewed as a composition of the cascade and the copy combiners. Our combiners are simple, efficient and practical.

Category / Keywords: applied cryptography, tolerant cryptography, foundations of cryptography, concrete security, commitment schemes

Publication Info: This is full version. Extended abstract version, titled `On Tolerant Cryptographic Constructions`, was presented in CT-RSA 2005.

Date: received 29 Aug 2002, last revised 20 Mar 2008

Contact author: amir herzberg at gmail com

Available format(s): PDF | BibTeX Citation

Note: This is draft of full version, being submitted to journal. Comments will be most appreciated.

Version: 20080320:205911 (All versions of this report)

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