An Efficient Non-interactive Universally Composable String-Commitment Scheme

Ryo NISHIMAKI; Eiichiro FUJISAKI; Keisuke TANAKA

doi:10.1587/transfun.E95.A.167

An Efficient Non-interactive Universally Composable String-Commitment Scheme

Ryo NISHIMAKI, Eiichiro FUJISAKI, Keisuke TANAKA

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This paper presents a new non-interactive string-commitment scheme that achieves universally composable security. Security is proven under the decisional composite residuosity (DCR) assumption (or the decisional Diffie-Hellman (DDH) assumption) in the common reference string (CRS) model. The universal composability (UC) is a very strong security notion. If cryptographic protocols are proven secure in the UC framework, then they remain secure even if they are composed with arbitrary protocols and polynomially many copies of the protocols are run concurrently. Many UC commitment schemes in the CRS model have been proposed, but they are either interactive commitment or bit-commitment (not string-commitment) schemes. We note, however, that although our scheme is the first non-interactive UC string-commitment scheme, a CRS is not reusable. We use an extension of all-but-one trapdoor functions (ABO-TDFs) proposed by Peikert and Waters at STOC 2008 as an essential building block. Our main idea is to extend (original deterministic) ABO-TDFs to probabilistic ones by using the homomorphic properties of their function indices. The function indices of ABO-TDFs consist of ciphertexts of homomorphic encryption schemes (such as ElGamal, and Damgåd-Jurik encryption). Therefore we can re-randomize the output of ABO-TDFs by re-randomization of ciphertexts. This is a new application of ABO-TDFs.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E95-A No.1 pp.167-175

Publication Date: 2012/01/01

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Online ISSN: 1745-1337

DOI: 10.1587/transfun.E95.A.167

Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)

Category: Secure Protocol

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Ryo NISHIMAKI, Eiichiro FUJISAKI, Keisuke TANAKA, "An Efficient Non-interactive Universally Composable String-Commitment Scheme" in IEICE TRANSACTIONS on Fundamentals, vol. E95-A, no. 1, pp. 167-175, January 2012, doi: 10.1587/transfun.E95.A.167.
Abstract: This paper presents a new non-interactive string-commitment scheme that achieves universally composable security. Security is proven under the decisional composite residuosity (DCR) assumption (or the decisional Diffie-Hellman (DDH) assumption) in the common reference string (CRS) model. The universal composability (UC) is a very strong security notion. If cryptographic protocols are proven secure in the UC framework, then they remain secure even if they are composed with arbitrary protocols and polynomially many copies of the protocols are run concurrently. Many UC commitment schemes in the CRS model have been proposed, but they are either interactive commitment or bit-commitment (not string-commitment) schemes. We note, however, that although our scheme is the first non-interactive UC string-commitment scheme, a CRS is not reusable. We use an extension of all-but-one trapdoor functions (ABO-TDFs) proposed by Peikert and Waters at STOC 2008 as an essential building block. Our main idea is to extend (original deterministic) ABO-TDFs to probabilistic ones by using the homomorphic properties of their function indices. The function indices of ABO-TDFs consist of ciphertexts of homomorphic encryption schemes (such as ElGamal, and Damgåd-Jurik encryption). Therefore we can re-randomize the output of ABO-TDFs by re-randomization of ciphertexts. This is a new application of ABO-TDFs.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E95.A.167/_p

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@ARTICLE{e95-a_1_167,
author={Ryo NISHIMAKI, Eiichiro FUJISAKI, Keisuke TANAKA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={An Efficient Non-interactive Universally Composable String-Commitment Scheme},
year={2012},
volume={E95-A},
number={1},
pages={167-175},
abstract={This paper presents a new non-interactive string-commitment scheme that achieves universally composable security. Security is proven under the decisional composite residuosity (DCR) assumption (or the decisional Diffie-Hellman (DDH) assumption) in the common reference string (CRS) model. The universal composability (UC) is a very strong security notion. If cryptographic protocols are proven secure in the UC framework, then they remain secure even if they are composed with arbitrary protocols and polynomially many copies of the protocols are run concurrently. Many UC commitment schemes in the CRS model have been proposed, but they are either interactive commitment or bit-commitment (not string-commitment) schemes. We note, however, that although our scheme is the first non-interactive UC string-commitment scheme, a CRS is not reusable. We use an extension of all-but-one trapdoor functions (ABO-TDFs) proposed by Peikert and Waters at STOC 2008 as an essential building block. Our main idea is to extend (original deterministic) ABO-TDFs to probabilistic ones by using the homomorphic properties of their function indices. The function indices of ABO-TDFs consist of ciphertexts of homomorphic encryption schemes (such as ElGamal, and Damgåd-Jurik encryption). Therefore we can re-randomize the output of ABO-TDFs by re-randomization of ciphertexts. This is a new application of ABO-TDFs.},
keywords={},
doi={10.1587/transfun.E95.A.167},
ISSN={1745-1337},
month={January},}

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TY - JOUR
TI - An Efficient Non-interactive Universally Composable String-Commitment Scheme
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 167
EP - 175
AU - Ryo NISHIMAKI
AU - Eiichiro FUJISAKI
AU - Keisuke TANAKA
PY - 2012
DO - 10.1587/transfun.E95.A.167
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E95-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 2012
AB - This paper presents a new non-interactive string-commitment scheme that achieves universally composable security. Security is proven under the decisional composite residuosity (DCR) assumption (or the decisional Diffie-Hellman (DDH) assumption) in the common reference string (CRS) model. The universal composability (UC) is a very strong security notion. If cryptographic protocols are proven secure in the UC framework, then they remain secure even if they are composed with arbitrary protocols and polynomially many copies of the protocols are run concurrently. Many UC commitment schemes in the CRS model have been proposed, but they are either interactive commitment or bit-commitment (not string-commitment) schemes. We note, however, that although our scheme is the first non-interactive UC string-commitment scheme, a CRS is not reusable. We use an extension of all-but-one trapdoor functions (ABO-TDFs) proposed by Peikert and Waters at STOC 2008 as an essential building block. Our main idea is to extend (original deterministic) ABO-TDFs to probabilistic ones by using the homomorphic properties of their function indices. The function indices of ABO-TDFs consist of ciphertexts of homomorphic encryption schemes (such as ElGamal, and Damgåd-Jurik encryption). Therefore we can re-randomize the output of ABO-TDFs by re-randomization of ciphertexts. This is a new application of ABO-TDFs.
ER -