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Iso/Iec Dis 18032 W - E 8 I 99 V d5 E 61 2 R i) /5 03 P a st 8 . si -1 D eh s/ is R it rd -d A s. : a ec D d rd nd -i r a ta so N a d /s /i A d an g 1 n st lo 8 T a l a a8 S t ul at c h s F c 6 e ( i/ b2 .a 0 Information technology iT h fc te d DRAFT INTERNATIONAL STANDARD .i 9- number generation ds c r a4 da - Technologies de l'information n 11 ta 6 /s -4 :/ f0 ps d ICS: 35.030 t 8 ISO/IEC JTC 1/SC 27 ht Voting begins on: 2019-02-08 — Techniques de sécurité ISO/IEC DIS 18032 — Security techniques Secretariat: V oting terminates on: 2019-05-03 — Génération de nombres premiers DIN — Prime THIS DOCUMENT IS A DRAFT CIRCULATED FOR COMMENT AND APPROVAL. IT IS THEREFORE SUBJECT TO CHANGE AND MAY NOT BE REFERRED TO AS AN INTERNATIONAL STANDARD UNTIL PUBLISHED AS SUCH. IN ADDITION TO THEIR EVALUATION AS BEING ACCEPTABLE FOR INDUSTRIAL, TECHNOLOGICAL, COMMERCIAL AND USER PURPOSES, DRAFT INTERNATIONAL STANDARDS MAY ON OCCASION HAVE TO BE CONSIDERED IN THE LIGHT OF THEIR POTENTIAL TO BECOME STANDARDS TO WHICH REFERENCE MAY BE MADE IN NATIONAL REGULATIONS. RECIPIENTS OF THIS DRAFT ARE INVITED TO SUBMIT, WITH THEIR COMMENTS, NOTIFICATION OF ANY RELEVANT PATENT RIGHTS OF WHICH THEY ARE AWARE AND TO PROVIDE SUPPORTING DOCUMENTATION. This document is circulated as received from the committee secretariat. ISO/IEC DIS 18032:2019(E) Reference number © ISO/IEC 2019 ISO/IEC DIS 18032:2019(E) W - E 8 I 99 V d5 E 61 2 R i) /5 03 P a st 8 . si -1 D eh s/ is R it rd -d A s. : a ec D d rd nd -i r a ta so N a nd /s /i A d ta g 81 T n s lo 8 S ta ll ta ca s u ca 6 h ( F i/ 2 e .a 0b iT h fc te d .i 9- ds c r a4 da - n 11 ta 6 /s -4 :/ 0 s df tp 8 ht © ISO/IEC 2019 All rights reserved. UnlessCOPYRIGHT otherwise specified, PROTECTED or required inDOCUMENT the context of its implementation, no part of this publication may be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below or ISO’s member body in the country of the requester. CP 401 • Ch. de Blandonnet 8 CH-1214ISO copyrightVernier, Geneva office Phone: +41 22 749 01 11 PublishedWebsite: inFax: Switzerland www.iso.org +41 22 749 09 47 Email: [email protected] ii © ISO/IEC 2019 – All rights reserved ISO/IEC DIS 18032 Contents Foreword ............................................................................................................................................................. v 1 Scope ...................................................................................................................................................... 1 2 Normative references ............................................................................................................................ 1 3 Terms and definitions ........................................................................................................................... 1 4 Symbols .................................................................................................................................................. 2 5 Trial division .......................................................................................................................................... 3 6 Probabilistic primality test.................................................................................................................... 4 6.1 General ................................................................................................................................................... 4 6.2 Requirements ......................................................................................................................................... 4 6.3 Miller-Rabin primality test..................................................................................................................... 4 7 Deterministic primality verification methods ..................................................................................... 6 7.1 General ................................................................................................................................................... 6 7.2 Elliptic curve primality proving algorithm .......................................................................................... 6 7.2.1 General ................................................................................................................................................... 6 7.2.2 Elliptic curve primality certificate generation .....................................................W - ............................... 6 7.2.3 Elliptic curve primality certificate verification ..................................................IE 98 .................................. 7 59 7.3 Primality certificate based on Shawe-Taylor'sV algorithm.....................................................d ............. 8 E 1 2 R ) 56 3 8 Prime number generation .................................................................................i t/ 0 .................................... 8 P .a is 18 8.1 General ...........................................................................................D h /s s- ........................................................ 8 e ds i 8.2 Requirements ........................................................................................R it r -d ................................................. 8 A s. : a ec 8.3 Using the Miller-Rabin primality testD ..............d ...................................................rd nd -i .................................. 9 r a ta so 8.3.1 General .........................................................................................N a nd /s /i .......................................................... 9 A d ta g 81 8.3.2 Random search .................................T n................................................... s lo 8 .................................................. 9 S ta ll ta ca 8.3.3 Incremental search ........................... s ...................................................u ca 6 .................................................. 9 h ( F i/ 2 8.3.4 Primes with an elliptic curvee primality certificat.a 0b e ............................................................................ 10 iT h fc 8.4 Using deterministic methods ..........................te d ................................................................................... 10 .i 9- 8.4.1 General .........................................................................................ds c ........................................................ 10 r a4 8.4.2 Shawe-Taylor's algorithm .........................da - .......................................................................................... 10 n 11 ta 6 Annex A (normative) Error probabilities/s ..................................-4 ...................................................................... 12 :/ f0 A.1 General ........................................s d ......................................................................................................... 12 tp 8 A.2 Worst-case error estimateht for t Miller-Rabin primality tests ........................................................... 12 A.3 Average-case error estimates for t Miller-Rabin primality tests ..................................................... 12 Annex B (normative) Generating primes with side conditions .................................................................... 14 B.1 General ................................................................................................................................................. 14 B.2 Congruence restrictions on primes ................................................................................................... 14 B.2.1 General ................................................................................................................................................. 14 B.2.2 Congruence restrictions and incremental or random search ........................................................ 14 B.2.3 Congruence restrictions and Shawe-Taylor’s algorithm ................................................................ 16 B.2.4 Generating primes in an interval ....................................................................................................... 16 Annex C (normative) Additional Random Number Generation methods .................................................... 17 C.1 General ................................................................................................................................................. 17 C.2 Simple conversion method ................................................................................................................ 17 C.3 Simple discard method (reverse order) ............................................................................................ 17 C.4 Simple modular method (reverse order) ........................................................................................... 17 Annex D (normative) Auxiliary methods ........................................................................................................ 18 D.1 Sieving procedure ............................................................................................................................... 18 D.2 Primality tests based on Pocklington’s Theorem ............................................................................ 18 D.2.1 General .................................................................................................................................................
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