Cryptosystems with a multi prime composite modulus

Shay Gueron; Nir Drucker

doi:https://doi.org/10.1109/CCNC.2018.8319159

Cryptosystems with a multi prime composite modulus

Shay Gueron, Nir Drucker

Department of Mathematics

University of Haifa

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Multi-Prime (MP)RSA is an RSA construction in which the public modulus is a product of more than two primes, and its private key operations can be accelerated by using the Chinese Reminder Theorem (CRT). While MPRSA has been studied extensively, only limited information is found for other MP constructions, such as Paillier cryptosystem. This paper shows how to extend the security proofs for Quadratic Residue Problem (QRP), Higher Residuosity Problem (HRP) and Decisional Composite Residuosity Problem (DCRP), formulated for a two-primes modulus, to a MP setting. For the Paillier cryptosystem, we demonstrate how this technique can speed up decryption by more than 17x.

Original language	American English
Title of host publication	CCNC 2018 - 2018 15th IEEE Annual Consumer Communications and Networking Conference
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1-7
Number of pages	7
ISBN (Electronic)	9781538647905
DOIs	https://doi.org/10.1109/CCNC.2018.8319159
State	Published - 16 Mar 2018
Event	15th IEEE Annual Consumer Communications and Networking Conference, CCNC 2018 - Las Vegas, United States Duration: 12 Jan 2018 → 15 Jan 2018

Conference

Conference	15th IEEE Annual Consumer Communications and Networking Conference, CCNC 2018
Country/Territory	United States
City	Las Vegas
Period	12/01/18 → 15/01/18

All Science Journal Classification (ASJC) codes

Computer Networks and Communications
Signal Processing
Media Technology

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https://doi.org/10.1109/CCNC.2018.8319159

Cite this

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title = "Cryptosystems with a multi prime composite modulus",

abstract = "Multi-Prime (MP)RSA is an RSA construction in which the public modulus is a product of more than two primes, and its private key operations can be accelerated by using the Chinese Reminder Theorem (CRT). While MPRSA has been studied extensively, only limited information is found for other MP constructions, such as Paillier cryptosystem. This paper shows how to extend the security proofs for Quadratic Residue Problem (QRP), Higher Residuosity Problem (HRP) and Decisional Composite Residuosity Problem (DCRP), formulated for a two-primes modulus, to a MP setting. For the Paillier cryptosystem, we demonstrate how this technique can speed up decryption by more than 17x.",

author = "Shay Gueron and Nir Drucker",

note = "Funding Information: This research was supported by the ISRAEL SCIENCE FOUNDATION (grant No. 1018/16), and by the BIU Center for Research in Applied Cryptography and Cyber Security in conjunction with the Israel National Cyber Bureau in the Prime Minister{\textquoteright}s Office. Publisher Copyright: {\textcopyright} 2018 IEEE.; 15th IEEE Annual Consumer Communications and Networking Conference, CCNC 2018 ; Conference date: 12-01-2018 Through 15-01-2018",

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doi = "https://doi.org/10.1109/CCNC.2018.8319159",

language = "American English",

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booktitle = "CCNC 2018 - 2018 15th IEEE Annual Consumer Communications and Networking Conference",

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Gueron, S & Drucker, N 2018, Cryptosystems with a multi prime composite modulus. in CCNC 2018 - 2018 15th IEEE Annual Consumer Communications and Networking Conference. Institute of Electrical and Electronics Engineers Inc., pp. 1-7, 15th IEEE Annual Consumer Communications and Networking Conference, CCNC 2018, Las Vegas, United States, 12/01/18. https://doi.org/10.1109/CCNC.2018.8319159

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T1 - Cryptosystems with a multi prime composite modulus

AU - Gueron, Shay

AU - Drucker, Nir

N1 - Funding Information: This research was supported by the ISRAEL SCIENCE FOUNDATION (grant No. 1018/16), and by the BIU Center for Research in Applied Cryptography and Cyber Security in conjunction with the Israel National Cyber Bureau in the Prime Minister’s Office. Publisher Copyright: © 2018 IEEE.

PY - 2018/3/16

Y1 - 2018/3/16

N2 - Multi-Prime (MP)RSA is an RSA construction in which the public modulus is a product of more than two primes, and its private key operations can be accelerated by using the Chinese Reminder Theorem (CRT). While MPRSA has been studied extensively, only limited information is found for other MP constructions, such as Paillier cryptosystem. This paper shows how to extend the security proofs for Quadratic Residue Problem (QRP), Higher Residuosity Problem (HRP) and Decisional Composite Residuosity Problem (DCRP), formulated for a two-primes modulus, to a MP setting. For the Paillier cryptosystem, we demonstrate how this technique can speed up decryption by more than 17x.

AB - Multi-Prime (MP)RSA is an RSA construction in which the public modulus is a product of more than two primes, and its private key operations can be accelerated by using the Chinese Reminder Theorem (CRT). While MPRSA has been studied extensively, only limited information is found for other MP constructions, such as Paillier cryptosystem. This paper shows how to extend the security proofs for Quadratic Residue Problem (QRP), Higher Residuosity Problem (HRP) and Decisional Composite Residuosity Problem (DCRP), formulated for a two-primes modulus, to a MP setting. For the Paillier cryptosystem, we demonstrate how this technique can speed up decryption by more than 17x.

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U2 - https://doi.org/10.1109/CCNC.2018.8319159

DO - https://doi.org/10.1109/CCNC.2018.8319159

M3 - Conference contribution

SP - 1

EP - 7

BT - CCNC 2018 - 2018 15th IEEE Annual Consumer Communications and Networking Conference

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 15th IEEE Annual Consumer Communications and Networking Conference, CCNC 2018

Y2 - 12 January 2018 through 15 January 2018

ER -

Cryptosystems with a multi prime composite modulus

Abstract

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All Science Journal Classification (ASJC) codes

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