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 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

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

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

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

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

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?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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