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Homomorphic Encryption Alexander Maximov. Slide title 44 pt Text and bullet level 1 minimum 24 pt Bullets level 2-5 minimum 20 pt Characters for Embedded.

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Presentation on theme: "Homomorphic Encryption Alexander Maximov. Slide title 44 pt Text and bullet level 1 minimum 24 pt Bullets level 2-5 minimum 20 pt Characters for Embedded."— Presentation transcript:

1 Homomorphic Encryption Alexander Maximov

2 Slide title 44 pt Text and bullet level 1 minimum 24 pt Bullets level 2-5 minimum 20 pt Characters for Embedded font: !"#$%&'()*+,-./ :; WXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡ ¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓ ÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷ øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪī ĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţ ŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲ ỳ–— ‘’‚“”„†‡…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞ ĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤ ŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰ αβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХ ЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦ ЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐә ǽ Ẁ ẁẂẃẄẅỲỳ№ Do not add objects or text in the footer area EAB/TZ Alexander Maximov | Public | © Ericsson AB 2013 | | Page 2 Overview History Partially Homomorphic Encryption Schemes HE Usage Scenarios Somewhat HE and Fully HE over the Integers Bootstrapping Technique Ciphertext Squashing Technique Ciphertext Reduction Technique Converting Somewhat HE to Fully HE Approximate GCD Problem Recent Research Results BGV FHE Scheme Leveled FHE with(out) Bootstrapping Performance, Implementations, Patents

3 Slide title 44 pt Text and bullet level 1 minimum 24 pt Bullets level 2-5 minimum 20 pt Characters for Embedded font: !"#$%&'()*+,-./ :; WXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡ ¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓ ÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷ øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪī ĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţ ŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲ ỳ–— ‘’‚“”„†‡…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞ ĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤ ŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰ αβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХ ЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦ ЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐә ǽ Ẁ ẁẂẃẄẅỲỳ№ Do not add objects or text in the footer area EAB/TZ Alexander Maximov | Public | © Ericsson AB 2013 | | Page 3 Introduction

4 Slide title 44 pt Text and bullet level 1 minimum 24 pt Bullets level 2-5 minimum 20 pt Characters for Embedded font: !"#$%&'()*+,-./ :; WXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡ ¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓ ÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷ øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪī ĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţ ŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲ ỳ–— ‘’‚“”„†‡…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞ ĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤ ŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰ αβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХ ЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦ ЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐә ǽ Ẁ ẁẂẃẄẅỲỳ№ Do not add objects or text in the footer area EAB/TZ Alexander Maximov | Public | © Ericsson AB 2013 | | Page 4 PartialLY HE

5 Slide title 44 pt Text and bullet level 1 minimum 24 pt Bullets level 2-5 minimum 20 pt Characters for Embedded font: !"#$%&'()*+,-./ :; WXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡ ¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓ ÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷ øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪī ĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţ ŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲ ỳ–— ‘’‚“”„†‡…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞ ĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤ ŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰ αβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХ ЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦ ЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐә ǽ Ẁ ẁẂẃẄẅỲỳ№ Do not add objects or text in the footer area EAB/TZ Alexander Maximov | Public | © Ericsson AB 2013 | | Page 5 HE Usage Scenarios

6 Slide title 44 pt Text and bullet level 1 minimum 24 pt Bullets level 2-5 minimum 20 pt Characters for Embedded font: !"#$%&'()*+,-./ :; WXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡ ¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓ ÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷ øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪī ĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţ ŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲ ỳ–— ‘’‚“”„†‡…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞ ĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤ ŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰ αβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХ ЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦ ЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐә ǽ Ẁ ẁẂẃẄẅỲỳ№ Do not add objects or text in the footer area EAB/TZ Alexander Maximov | Public | © Ericsson AB 2013 | | Page 6 Real-Life Usage

7 Slide title 44 pt Text and bullet level 1 minimum 24 pt Bullets level 2-5 minimum 20 pt Characters for Embedded font: !"#$%&'()*+,-./ :; WXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡ ¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓ ÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷ øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪī ĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţ ŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲ ỳ–— ‘’‚“”„†‡…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞ ĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤ ŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰ αβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХ ЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦ ЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐә ǽ Ẁ ẁẂẃẄẅỲỳ№ Do not add objects or text in the footer area EAB/TZ Alexander Maximov | Public | © Ericsson AB 2013 | | Page 7 Does Fully Homomorphic Encryption Ever Exists?

8 Slide title 44 pt Text and bullet level 1 minimum 24 pt Bullets level 2-5 minimum 20 pt Characters for Embedded font: !"#$%&'()*+,-./ :; WXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡ ¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓ ÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷ øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪī ĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţ ŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲ ỳ–— ‘’‚“”„†‡…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞ ĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤ ŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰ αβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХ ЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦ ЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐә ǽ Ẁ ẁẂẃẄẅỲỳ№ Do not add objects or text in the footer area EAB/TZ Alexander Maximov | Public | © Ericsson AB 2013 | | Page 8 “Holy Grail” for 30 years

9 Slide title 44 pt Text and bullet level 1 minimum 24 pt Bullets level 2-5 minimum 20 pt Characters for Embedded font: !"#$%&'()*+,-./ :; WXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡ ¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓ ÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷ øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪī ĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţ ŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲ ỳ–— ‘’‚“”„†‡…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞ ĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤ ŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰ αβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХ ЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦ ЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐә ǽ Ẁ ẁẂẃẄẅỲỳ№ Do not add objects or text in the footer area EAB/TZ Alexander Maximov | Public | © Ericsson AB 2013 | | Page 9 Types of HE Schemes

10 Slide title 44 pt Text and bullet level 1 minimum 24 pt Bullets level 2-5 minimum 20 pt Characters for Embedded font: !"#$%&'()*+,-./ :; WXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡ ¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓ ÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷ øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪī ĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţ ŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲ ỳ–— ‘’‚“”„†‡…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞ ĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤ ŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰ αβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХ ЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦ ЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐә ǽ Ẁ ẁẂẃẄẅỲỳ№ Do not add objects or text in the footer area EAB/TZ Alexander Maximov | Public | © Ericsson AB 2013 | | Page 10 SHE over the Integers

11 Slide title 44 pt Text and bullet level 1 minimum 24 pt Bullets level 2-5 minimum 20 pt Characters for Embedded font: !"#$%&'()*+,-./ :; WXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡ ¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓ ÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷ øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪī ĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţ ŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲ ỳ–— ‘’‚“”„†‡…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞ ĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤ ŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰ αβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХ ЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦ ЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐә ǽ Ẁ ẁẂẃẄẅỲỳ№ Do not add objects or text in the footer area EAB/TZ Alexander Maximov | Public | © Ericsson AB 2013 | | Page 11 SHE over the Integers

12 Slide title 44 pt Text and bullet level 1 minimum 24 pt Bullets level 2-5 minimum 20 pt Characters for Embedded font: !"#$%&'()*+,-./ :; WXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡ ¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓ ÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷ øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪī ĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţ ŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲ ỳ–— ‘’‚“”„†‡…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞ ĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤ ŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰ αβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХ ЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦ ЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐә ǽ Ẁ ẁẂẃẄẅỲỳ№ Do not add objects or text in the footer area EAB/TZ Alexander Maximov | Public | © Ericsson AB 2013 | | Page 12 SHE over the Integers

13 Slide title 44 pt Text and bullet level 1 minimum 24 pt Bullets level 2-5 minimum 20 pt Characters for Embedded font: !"#$%&'()*+,-./ :; WXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡ ¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓ ÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷ øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪī ĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţ ŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲ ỳ–— ‘’‚“”„†‡…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞ ĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤ ŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰ αβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХ ЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦ ЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐә ǽ Ẁ ẁẂẃẄẅỲỳ№ Do not add objects or text in the footer area EAB/TZ Alexander Maximov | Public | © Ericsson AB 2013 | | Page 13 Noise Count

14 Slide title 44 pt Text and bullet level 1 minimum 24 pt Bullets level 2-5 minimum 20 pt Characters for Embedded font: !"#$%&'()*+,-./ :; WXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡ ¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓ ÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷ øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪī ĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţ ŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲ ỳ–— ‘’‚“”„†‡…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞ ĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤ ŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰ αβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХ ЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦ ЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐә ǽ Ẁ ẁẂẃẄẅỲỳ№ Do not add objects or text in the footer area EAB/TZ Alexander Maximov | Public | © Ericsson AB 2013 | | Page 14 SHE over the Integers

15 Slide title 44 pt Text and bullet level 1 minimum 24 pt Bullets level 2-5 minimum 20 pt Characters for Embedded font: !"#$%&'()*+,-./ :; WXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡ ¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓ ÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷ øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪī ĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţ ŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲ ỳ–— ‘’‚“”„†‡…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞ ĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤ ŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰ αβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХ ЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦ ЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐә ǽ Ẁ ẁẂẃẄẅỲỳ№ Do not add objects or text in the footer area EAB/TZ Alexander Maximov | Public | © Ericsson AB 2013 | | Page 15 Ciphertext Reduction

16 Slide title 44 pt Text and bullet level 1 minimum 24 pt Bullets level 2-5 minimum 20 pt Characters for Embedded font: !"#$%&'()*+,-./ :; WXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡ ¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓ ÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷ øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪī ĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţ ŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲ ỳ–— ‘’‚“”„†‡…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞ ĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤ ŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰ αβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХ ЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦ ЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐә ǽ Ẁ ẁẂẃẄẅỲỳ№ Do not add objects or text in the footer area EAB/TZ Alexander Maximov | Public | © Ericsson AB 2013 | | Page 16 Bootstrapping

17 Slide title 44 pt Text and bullet level 1 minimum 24 pt Bullets level 2-5 minimum 20 pt Characters for Embedded font: !"#$%&'()*+,-./ :; WXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡ ¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓ ÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷ øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪī ĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţ ŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲ ỳ–— ‘’‚“”„†‡…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞ ĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤ ŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰ αβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХ ЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦ ЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐә ǽ Ẁ ẁẂẃẄẅỲỳ№ Do not add objects or text in the footer area EAB/TZ Alexander Maximov | Public | © Ericsson AB 2013 | | Page 17 SHE  FHE over the Integers

18 Slide title 44 pt Text and bullet level 1 minimum 24 pt Bullets level 2-5 minimum 20 pt Characters for Embedded font: !"#$%&'()*+,-./ :; WXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡ ¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓ ÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷ øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪī ĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţ ŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲ ỳ–— ‘’‚“”„†‡…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞ ĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤ ŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰ αβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХ ЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦ ЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐә ǽ Ẁ ẁẂẃẄẅỲỳ№ Do not add objects or text in the footer area EAB/TZ Alexander Maximov | Public | © Ericsson AB 2013 | | Page 18 Squashing Technique

19 Slide title 44 pt Text and bullet level 1 minimum 24 pt Bullets level 2-5 minimum 20 pt Characters for Embedded font: !"#$%&'()*+,-./ :; WXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡ ¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓ ÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷ øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪī ĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţ ŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲ ỳ–— ‘’‚“”„†‡…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞ ĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤ ŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰ αβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХ ЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦ ЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐә ǽ Ẁ ẁẂẃẄẅỲỳ№ Do not add objects or text in the footer area EAB/TZ Alexander Maximov | Public | © Ericsson AB 2013 | | Page 19 Security. Approximate GCD

20 Slide title 44 pt Text and bullet level 1 minimum 24 pt Bullets level 2-5 minimum 20 pt Characters for Embedded font: !"#$%&'()*+,-./ :; WXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡ ¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓ ÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷ øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪī ĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţ ŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲ ỳ–— ‘’‚“”„†‡…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞ ĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤ ŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰ αβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХ ЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦ ЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐә ǽ Ẁ ẁẂẃẄẅỲỳ№ Do not add objects or text in the footer area EAB/TZ Alexander Maximov | Public | © Ericsson AB 2013 | | Page 20 Security. Approximate GCD

21 Slide title 44 pt Text and bullet level 1 minimum 24 pt Bullets level 2-5 minimum 20 pt Characters for Embedded font: !"#$%&'()*+,-./ :; WXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡ ¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓ ÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷ øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪī ĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţ ŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲ ỳ–— ‘’‚“”„†‡…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞ ĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤ ŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰ αβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХ ЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦ ЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐә ǽ Ẁ ẁẂẃẄẅỲỳ№ Do not add objects or text in the footer area EAB/TZ Alexander Maximov | Public | © Ericsson AB 2013 | | Page 21 Security. Approximate GCD

22 Slide title 44 pt Text and bullet level 1 minimum 24 pt Bullets level 2-5 minimum 20 pt Characters for Embedded font: !"#$%&'()*+,-./ :; WXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡ ¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓ ÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷ øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪī ĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţ ŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲ ỳ–— ‘’‚“”„†‡…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞ ĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤ ŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰ αβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХ ЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦ ЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐә ǽ Ẁ ẁẂẃẄẅỲỳ№ Do not add objects or text in the footer area EAB/TZ Alexander Maximov | Public | © Ericsson AB 2013 | | Page 22 Security. Approximate GCD

23 Slide title 44 pt Text and bullet level 1 minimum 24 pt Bullets level 2-5 minimum 20 pt Characters for Embedded font: !"#$%&'()*+,-./ :; WXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡ ¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓ ÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷ øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪī ĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţ ŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲ ỳ–— ‘’‚“”„†‡…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞ ĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤ ŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰ αβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХ ЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦ ЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐә ǽ Ẁ ẁẂẃẄẅỲỳ№ Do not add objects or text in the footer area EAB/TZ Alexander Maximov | Public | © Ericsson AB 2013 | | Page 23 Security. Approximate GCD

24 Slide title 44 pt Text and bullet level 1 minimum 24 pt Bullets level 2-5 minimum 20 pt Characters for Embedded font: !"#$%&'()*+,-./ :; WXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡ ¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓ ÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷ øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪī ĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţ ŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲ ỳ–— ‘’‚“”„†‡…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞ ĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤ ŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰ αβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХ ЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦ ЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐә ǽ Ẁ ẁẂẃẄẅỲỳ№ Do not add objects or text in the footer area EAB/TZ Alexander Maximov | Public | © Ericsson AB 2013 | | Page 24 New Recent Research

25 Slide title 44 pt Text and bullet level 1 minimum 24 pt Bullets level 2-5 minimum 20 pt Characters for Embedded font: !"#$%&'()*+,-./ :; WXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡ ¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓ ÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷ øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪī ĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţ ŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲ ỳ–— ‘’‚“”„†‡…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞ ĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤ ŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰ αβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХ ЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦ ЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐә ǽ Ẁ ẁẂẃẄẅỲỳ№ Do not add objects or text in the footer area EAB/TZ Alexander Maximov | Public | © Ericsson AB 2013 | | Page 25 BGV: Leveled FHE Scheme

26 Slide title 44 pt Text and bullet level 1 minimum 24 pt Bullets level 2-5 minimum 20 pt Characters for Embedded font: !"#$%&'()*+,-./ :; WXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡ ¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓ ÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷ øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪī ĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţ ŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲ ỳ–— ‘’‚“”„†‡…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞ ĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤ ŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰ αβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХ ЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦ ЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐә ǽ Ẁ ẁẂẃẄẅỲỳ№ Do not add objects or text in the footer area EAB/TZ Alexander Maximov | Public | © Ericsson AB 2013 | | Page 26 BGV: Leveled FHE Scheme

27 Slide title 44 pt Text and bullet level 1 minimum 24 pt Bullets level 2-5 minimum 20 pt Characters for Embedded font: !"#$%&'()*+,-./ :; WXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡ ¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓ ÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷ øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪī ĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţ ŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲ ỳ–— ‘’‚“”„†‡…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞ ĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤ ŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰ αβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХ ЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦ ЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐә ǽ Ẁ ẁẂẃẄẅỲỳ№ Do not add objects or text in the footer area EAB/TZ Alexander Maximov | Public | © Ericsson AB 2013 | | Page 27 Performance

28 Slide title 44 pt Text and bullet level 1 minimum 24 pt Bullets level 2-5 minimum 20 pt Characters for Embedded font: !"#$%&'()*+,-./ :; WXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡ ¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓ ÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷ øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪī ĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţ ŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲ ỳ–— ‘’‚“”„†‡…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞ ĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤ ŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰ αβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХ ЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦ ЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐә ǽ Ẁ ẁẂẃẄẅỲỳ№ Do not add objects or text in the footer area EAB/TZ Alexander Maximov | Public | © Ericsson AB 2013 | | Page 28 Evaluation of AES

29 Slide title 44 pt Text and bullet level 1 minimum 24 pt Bullets level 2-5 minimum 20 pt Characters for Embedded font: !"#$%&'()*+,-./ :; WXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡ ¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓ ÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷ øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪī ĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţ ŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲ ỳ–— ‘’‚“”„†‡…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞ ĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤ ŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰ αβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХ ЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦ ЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐә ǽ Ẁ ẁẂẃẄẅỲỳ№ Do not add objects or text in the footer area EAB/TZ Alexander Maximov | Public | © Ericsson AB 2013 | | Page 29 HElib

30 Slide title 44 pt Text and bullet level 1 minimum 24 pt Bullets level 2-5 minimum 20 pt Characters for Embedded font: !"#$%&'()*+,-./ :; WXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡ ¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓ ÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷ øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪī ĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţ ŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲ ỳ–— ‘’‚“”„†‡…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞ ĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤ ŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰ αβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХ ЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦ ЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐә ǽ Ẁ ẁẂẃẄẅỲỳ№ Do not add objects or text in the footer area EAB/TZ Alexander Maximov | Public | © Ericsson AB 2013 | | Page 30 Patents Activity

31 Slide title 44 pt Text and bullet level 1 minimum 24 pt Bullets level 2-5 minimum 20 pt Characters for Embedded font: !"#$%&'()*+,-./ :; WXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡ ¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓ ÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷ øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪī ĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţ ŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲ ỳ–— ‘’‚“”„†‡…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞ ĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤ ŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰ αβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХ ЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦ ЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐә ǽ Ẁ ẁẂẃẄẅỲỳ№ Do not add objects or text in the footer area EAB/TZ Alexander Maximov | Public | © Ericsson AB 2013 | | Page 31

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