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                           <rdf:li><rdf:Description xmpDM:name="Digital Signature Raj Jain Washington University in Saint Louis Saint Louis, MO 63130 Jain@cse.wustl.edu" xmpDM:startTime="0" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Audio/Video recordings of this lecture are available at: http://www.cse.wustl.edu/~jain/cse571-17/" xmpDM:startTime="0" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="0" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Overview Digital Signatures ElGamal Digital Signature Scheme Schnorr Digital Signature Scheme Digital Signature Standard (DSS) These slides are based partly" xmpDM:startTime="17700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="on Lawrie Brown’s slides supplied with William Stallings’s book “Cryptography and Network Security: Principles and Practice,” 7th Ed, 2017." xmpDM:startTime="17700" 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xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Digital Signatures Verify author, date &amp; time of signature Authenticate message contents Can be verified by third parties to resolve" xmpDM:startTime="89833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="disputes Ref: http://en.wikipedia.org/wiki/Non-repudiation," xmpDM:startTime="89833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="http://en.wikipedia.org/wiki/Digital_signature," xmpDM:startTime="89833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="http://en.wikipedia.org/wiki/Digital_signatures_and_law" xmpDM:startTime="89833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="89833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Digital Signature Model" xmpDM:startTime="108367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Attacks In the order of Increasing severity." xmpDM:startTime="135300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="C=Attacker, A=Victim Key-only attack: C only knows A’s public key Known message attack: C has a set of messages, signatures" xmpDM:startTime="135300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Generic chosen message attack: C obtains A’s signatures on messages selected without knowledge of A’s public key Directed chosen message" xmpDM:startTime="135300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="attack: C obtains A’s signatures on messages selected after knowing A’s public key Adaptive chosen message attack: C may request" xmpDM:startTime="135300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="signatures on messages depending upon previous message-signature pairs" xmpDM:startTime="135300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Forgeries Total break: C knows A’s private key Universal forgery: C can generate A’s signatures on any message Selective forgery:" xmpDM:startTime="284433" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="C can generate A’s signature for a particular message chosen by C Existential forgery: C can generate A’s signature for" xmpDM:startTime="284433" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="a message not chosen by C" xmpDM:startTime="284433" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Attacks In the order of Increasing severity." xmpDM:startTime="294133" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="C=Attacker, A=Victim Key-only attack: C only knows A’s public key Known message attack: C has a set of messages, signatures" xmpDM:startTime="294133" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Generic chosen message attack: C obtains A’s signatures on messages selected without knowledge of A’s public key Directed chosen message" xmpDM:startTime="294133" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="attack: C obtains A’s signatures on messages selected after knowing A’s public key Adaptive chosen message attack: C may request" xmpDM:startTime="294133" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="signatures on messages depending upon previous message-signature pairs" xmpDM:startTime="294133" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Forgeries Total break: C knows A’s private key Universal forgery: C can generate A’s signatures on any message Selective forgery:" xmpDM:startTime="365433" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="C can generate A’s signature for a particular message chosen by C Existential forgery: C can generate A’s signature for" xmpDM:startTime="365433" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="a message not chosen by C" xmpDM:startTime="365433" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Digital Signature Requirements Must depend on the message signed Must use information unique to sender To prevent both forgery and" xmpDM:startTime="500767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="denial Must be relatively easy to produce Must be relatively easy to recognize &amp; verify Directed  Recipient can verify" xmpDM:startTime="500767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Arbitrated  Anyone can verify Be computationally infeasible to forge With new message for existing digital signature With fraudulent digital" xmpDM:startTime="500767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="signature for given message Be able to retain a copy of the signature in storage Ref: http://en.wikipedia.org/wiki/Electronic_signature" xmpDM:startTime="500767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="500767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="663967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="806800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1041133" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1053900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="ElGamal Signature Example GF(19) q=19 and a=10 Alice computes her key: A chooses xA=16 &amp; computes yA=1016 mod 19 =" xmpDM:startTime="1083200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4 Alice signs message with hash m=14 as (3,4): Choosing random K=5 which has gcd(18,5)=1 Computing S1 = 105 mod" xmpDM:startTime="1083200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="19 = 3 Finding K-1 mod (q-1) = 5-1 mod 18 = 11 Computing S2 = 11(14-163) mod 18 =" xmpDM:startTime="1083200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4 Any user B can verify the signature by computing V1 = am mod q = 1014 mod 19 =" xmpDM:startTime="1083200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="16 V2 =yAS1S1S2mod q=4334 = 5184 mod 19 = 16 Since 16 = 16, the signature is valid" xmpDM:startTime="1083200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1184033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="ElGamal Signature Example GF(19) q=19 and a=10 Alice computes her key: A chooses xA=16 &amp; computes yA=1016 mod 19 =" xmpDM:startTime="1188833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4 Alice signs message with hash m=14 as (3,4): Choosing random K=5 which has gcd(18,5)=1 Computing S1 = 105 mod" xmpDM:startTime="1188833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="19 = 3 Finding K-1 mod (q-1) = 5-1 mod 18 = 11 Computing S2 = 11(14-163) mod 18 =" xmpDM:startTime="1188833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4 Any user B can verify the signature by computing V1 = am mod q = 1014 mod 19 =" xmpDM:startTime="1188833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="16 V2 =yAS1S1S2mod q=4334 = 5184 mod 19 = 16 Since 16 = 16, the signature is valid" xmpDM:startTime="1188833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1262333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="ElGamal Signature Example GF(19) q=19 and a=10 Alice computes her key: A chooses xA=16 &amp; computes yA=1016 mod 19 =" xmpDM:startTime="1283333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4 Alice signs message with hash m=14 as (3,4): Choosing random K=5 which has gcd(18,5)=1 Computing S1 = 105 mod" xmpDM:startTime="1283333" 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gcd(18,5)=1 Computing S1 = 105 mod" xmpDM:startTime="1305267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="19 = 3 Finding K-1 mod (q-1) = 5-1 mod 18 = 11 Computing S2 = 11(14-163) mod 18 =" xmpDM:startTime="1305267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4 Any user B can verify the signature by computing V1 = am mod q = 1014 mod 19 =" xmpDM:startTime="1305267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="16 V2 =yAS1S1S2mod q=4334 = 5184 mod 19 = 16 Since 16 = 16, the signature is valid" xmpDM:startTime="1305267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1330167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="ElGamal Signature Example GF(19) q=19 and a=10 Alice computes her key: A chooses xA=16 &amp; computes yA=1016 mod 19 =" xmpDM:startTime="1355700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4 Alice signs message with hash m=14 as (3,4): Choosing random K=5 which has gcd(18,5)=1 Computing S1 = 105 mod" xmpDM:startTime="1355700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="19 = 3 Finding K-1 mod (q-1) = 5-1 mod 18 = 11 Computing S2 = 11(14-163) mod 18 =" xmpDM:startTime="1355700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4 Any user B can verify the signature by computing V1 = am mod q = 1014 mod 19 =" xmpDM:startTime="1355700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="16 V2 =yAS1S1S2mod q=4334 = 5184 mod 19 = 16 Since 16 = 16, the signature is valid" xmpDM:startTime="1355700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1356400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="ElGamal Signature Example GF(19) q=19 and a=10 Alice computes her key: A chooses xA=16 &amp; computes yA=1016 mod 19 =" xmpDM:startTime="1522733" 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xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4 Any user B can verify the signature by computing V1 = am mod q = 1014 mod 19 =" xmpDM:startTime="1587467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="16 V2 =yAS1S1S2mod q=4334 = 5184 mod 19 = 16 Since 16 = 16, the signature is valid" xmpDM:startTime="1587467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1587833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1588767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1719000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1724900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1730967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="ElGamal Signature Example GF(19) q=19 and a=10 Alice computes her key: A chooses xA=16 &amp; computes yA=1016 mod 19 =" xmpDM:startTime="1731367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4 Alice signs message with hash m=14 as (3,4): Choosing random K=5 which has gcd(18,5)=1 Computing S1 = 105 mod" xmpDM:startTime="1731367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="19 = 3 Finding K-1 mod (q-1) = 5-1 mod 18 = 11 Computing S2 = 11(14-163) mod 18 =" xmpDM:startTime="1731367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4 Any user B can verify the signature by computing V1 = am mod q = 1014 mod 19 =" xmpDM:startTime="1731367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="16 V2 =yAS1S1S2mod q=4334 = 5184 mod 19 = 16 Since 16 = 16, the signature is valid" xmpDM:startTime="1731367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1731967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="ElGamal Signature Example GF(19) q=19 and a=10 Alice computes her key: A chooses xA=16 &amp; computes yA=1016 mod 19 =" xmpDM:startTime="1741267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4 Alice signs message with hash m=14 as (3,4): Choosing random K=5 which has gcd(18,5)=1 Computing S1 = 105 mod" xmpDM:startTime="1741267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="19 = 3 Finding K-1 mod (q-1) = 5-1 mod 18 = 11 Computing S2 = 11(14-163) mod 18 =" xmpDM:startTime="1741267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4 Any user B can verify the signature by computing V1 = am mod q = 1014 mod 19 =" xmpDM:startTime="1741267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="16 V2 =yAS1S1S2mod q=4334 = 5184 mod 19 = 16 Since 16 = 16, the signature is valid" xmpDM:startTime="1741267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1743267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1821333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1841533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1962400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2019633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2023067" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2088667" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2134033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Digital Signature Standard (DSS) US Govt approved signature scheme Designed by NIST &amp; NSA in early 90's Published as FIPS-186" xmpDM:startTime="2168067" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="in 1991 Revised in 1993, 1996 &amp; then 2000 Uses the SHA hash algorithm DSS is the standard, DSA is" xmpDM:startTime="2168067" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="the algorithm FIPS 186-2 (2000) includes alternative RSA &amp; elliptic curve signature variants DSA is digital signature only Ref: http://en.wikipedia.org/wiki/Digital_Signature_Algorithm" xmpDM:startTime="2168067" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2168067" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2169367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2169667" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2187933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Digital Signature Standard (DSS) US Govt approved signature scheme Designed by NIST &amp; NSA in early 90's Published as FIPS-186" xmpDM:startTime="2188667" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="in 1991 Revised in 1993, 1996 &amp; then 2000 Uses the SHA hash algorithm DSS is the standard, DSA is" xmpDM:startTime="2188667" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="the algorithm FIPS 186-2 (2000) includes alternative RSA &amp; elliptic curve signature variants DSA is digital signature only Ref: http://en.wikipedia.org/wiki/Digital_Signature_Algorithm" xmpDM:startTime="2188667" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2188667" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Digital Signature Algorithm (DSA) Creates a 320 bit signature With 512-1024 bit security Smaller and faster than RSA A digital" xmpDM:startTime="2272600" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="signature scheme only Security depends on difficulty of computing discrete logarithms Variant of ElGamal &amp; Schnorr schemes" xmpDM:startTime="2272600" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2329500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2480867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2537067" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Digital Signature Algorithm (DSA) Creates a 320 bit signature With 512-1024 bit security Smaller and faster than RSA A digital" xmpDM:startTime="2537600" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="signature scheme only Security depends on difficulty of computing discrete logarithms Variant of ElGamal &amp; Schnorr schemes" xmpDM:startTime="2537600" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Digital Signature Standard (DSS) US Govt approved signature scheme Designed by NIST &amp; NSA in early 90's Published as FIPS-186" xmpDM:startTime="2538067" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="in 1991 Revised in 1993, 1996 &amp; then 2000 Uses the SHA hash algorithm DSS is the standard, DSA is" xmpDM:startTime="2538067" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="the algorithm FIPS 186-2 (2000) includes alternative RSA &amp; elliptic curve signature variants DSA is digital signature only Ref: http://en.wikipedia.org/wiki/Digital_Signature_Algorithm" xmpDM:startTime="2538067" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2538067" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2538500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2543667" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="ElGamal Signature Example GF(19) q=19 and a=10 Alice computes her key: A chooses xA=16 &amp; computes yA=1016 mod 19 =" xmpDM:startTime="2543967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4 Alice signs message with hash m=14 as (3,4): Choosing random K=5 which has gcd(18,5)=1 Computing S1 = 105 mod" xmpDM:startTime="2543967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="19 = 3 Finding K-1 mod (q-1) = 5-1 mod 18 = 11 Computing S2 = 11(14-163) mod 18 =" xmpDM:startTime="2543967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4 Any user B can verify the signature by computing V1 = am mod q = 1014 mod 19 =" xmpDM:startTime="2543967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="16 V2 =yAS1S1S2mod q=4334 = 5184 mod 19 = 16 Since 16 = 16, the signature is valid" xmpDM:startTime="2543967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2549633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2552733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2555567" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="ElGamal Signature Example GF(19) q=19 and a=10 Alice computes her key: A chooses xA=16 &amp; computes yA=1016 mod 19 =" xmpDM:startTime="2585167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4 Alice signs message with hash m=14 as (3,4): Choosing random K=5 which has gcd(18,5)=1 Computing S1 = 105 mod" xmpDM:startTime="2585167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="19 = 3 Finding K-1 mod (q-1) = 5-1 mod 18 = 11 Computing S2 = 11(14-163) mod 18 =" xmpDM:startTime="2585167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4 Any user B can verify the signature by computing V1 = am mod q = 1014 mod 19 =" xmpDM:startTime="2585167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="16 V2 =yAS1S1S2mod q=4334 = 5184 mod 19 = 16 Since 16 = 16, the signature is valid" xmpDM:startTime="2585167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2585667" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2586100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Digital Signature Standard (DSS) US Govt approved signature scheme Designed by NIST &amp; NSA in early 90's Published as FIPS-186" xmpDM:startTime="2586567" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="in 1991 Revised in 1993, 1996 &amp; then 2000 Uses the SHA hash algorithm DSS is the standard, DSA is" xmpDM:startTime="2586567" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="the algorithm FIPS 186-2 (2000) includes alternative RSA &amp; elliptic curve signature variants DSA is digital signature only Ref: http://en.wikipedia.org/wiki/Digital_Signature_Algorithm" xmpDM:startTime="2586567" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2586567" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Digital Signature Algorithm (DSA) Creates a 320 bit signature With 512-1024 bit security Smaller and faster than RSA A digital" xmpDM:startTime="2587000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="signature scheme only Security depends on difficulty of computing discrete logarithms Variant of ElGamal &amp; Schnorr schemes" xmpDM:startTime="2587000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2587533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2588333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="DSA Signature Verification To verify a signature, recipient computes: w = s-1 mod q u1= [H(M)w ] mod q u2=" xmpDM:startTime="2625833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="(rw) mod q v = [(gu1 yu2) mod p ] mod q If v=r then signature is verified" xmpDM:startTime="2625833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2649333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="DSA Signature Verification To verify a signature, recipient computes: w = s-1 mod q u1= [H(M)w ] mod q u2=" xmpDM:startTime="2674033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="(rw) mod q v = [(gu1 yu2) mod p ] mod q If v=r then signature is verified" xmpDM:startTime="2674033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="DSS vs." xmpDM:startTime="2748167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="RSA Signatures PUG = Global Public Key k = Per message secret key PRa = x" xmpDM:startTime="2748167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Summary Digital signature depends upon the message and some information unique to the signer to prevent forgery and denial." xmpDM:startTime="2813333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Anyone should be able to verify." xmpDM:startTime="2813333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="ElGamal/Schnorr/DSA signatures use a per-message secret key and are based on exponentiation DSA produces a 320 bit signature" xmpDM:startTime="2813333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Homework 13 DSA specifies that if signature generation process results in a value of s=0, a new value of k" xmpDM:startTime="2847667" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="should be generated and the signature should be recalculated." xmpDM:startTime="2847667" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Why? Suppose Alice signed a message M using DSA with a specific k value and then the k value was" xmpDM:startTime="2847667" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="compromised." xmpDM:startTime="2847667" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Can Alice still use her private key for future digital signatures? Hint: Show that the private key of the signer" xmpDM:startTime="2847667" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="can be easily computed in both of the above cases." xmpDM:startTime="2847667" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2847667" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Lab 13: Nessus In this lab, you will use Nessus software to scan vulnerabilities in your network Nessus is a" xmpDM:startTime="2912733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="common vulnerability scanning platform for auditors and security analysts." xmpDM:startTime="2912733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="You can download Nessus from https://www.tenable.com/products/nessus/select-your-operating-system" xmpDM:startTime="2912733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="You can do the lab on windows, Mac, or Kali (might not work from USB boot) Ref: https://en.wikipedia.org/wiki/Nessus_(software)" xmpDM:startTime="2912733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2912733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Acronyms DSA Digital Signature Algorithm DSS Digital Signature Standard FIPS Federal Information Processing Standard GF Galois Field MIME Multipurpose Internet" xmpDM:startTime="2948767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Mail Extension NIST National Institute of Technology NSA National Security Agency PR Private Key PU Public Key RSA Rivest, Shamir," xmpDM:startTime="2948767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and Adleman SHA Secure Hash Algorithm" xmpDM:startTime="2948767" xmpDM:duration="1000"/></rdf:li></rdf:Seq>
                     </xmpDM:markers>
                  </rdf:Description>
               </rdf:li>
               <rdf:li>
                  <rdf:Description xmpDM:trackType="TableOfContents" xmpDM:frameRate="f1000" xmpDM:trackName="Table of Contents">
                     <xmpDM:markers>
                        <rdf:Seq>
                           <rdf:li><rdf:Description xmpDM:name="Digital Signature" xmpDM:startTime="0" tscDM:image="l_13ds_Thumbnails.png" tscDM:imageindex="0" tscDM:imageoffset="0" tscDM:imagerect="0, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Overview" xmpDM:startTime="17700" tscDM:image="l_13ds_Thumbnails.png" tscDM:imageindex="1" tscDM:imageoffset="0" tscDM:imagerect="75, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Digital Signatures" xmpDM:startTime="33967" tscDM:image="l_13ds_Thumbnails.png" tscDM:imageindex="2" tscDM:imageoffset="0" tscDM:imagerect="150, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Digital Signature Model" xmpDM:startTime="87867" tscDM:image="l_13ds_Thumbnails.png" tscDM:imageindex="3" tscDM:imageoffset="0" tscDM:imagerect="225, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Digital Signatures" xmpDM:startTime="89833" tscDM:image="l_13ds_Thumbnails.png" tscDM:imageindex="4" tscDM:imageoffset="0" tscDM:imagerect="300, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Digital Signature Model" xmpDM:startTime="108367" tscDM:image="l_13ds_Thumbnails.png" tscDM:imageindex="5" tscDM:imageoffset="0" tscDM:imagerect="375, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Attacks" xmpDM:startTime="135300" tscDM:image="l_13ds_Thumbnails.png" tscDM:imageindex="6" tscDM:imageoffset="0" tscDM:imagerect="450, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Forgeries" xmpDM:startTime="284433" tscDM:image="l_13ds_Thumbnails.png" tscDM:imageindex="7" tscDM:imageoffset="0" tscDM:imagerect="525, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Attacks" xmpDM:startTime="294133" tscDM:image="l_13ds_Thumbnails.png" tscDM:imageindex="8" tscDM:imageoffset="0" tscDM:imagerect="600, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Forgeries" xmpDM:startTime="365433" tscDM:image="l_13ds_Thumbnails.png" tscDM:imageindex="9" tscDM:imageoffset="0" tscDM:imagerect="675, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Digital Signature Requirements" xmpDM:startTime="500767" tscDM:image="l_13ds_Thumbnails.png" tscDM:imageindex="10" tscDM:imageoffset="0" tscDM:imagerect="750, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="ElGamal Digital Signatures" xmpDM:startTime="663967" tscDM:image="l_13ds_Thumbnails.png" tscDM:imageindex="11" tscDM:imageoffset="0" tscDM:imagerect="825, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="ElGamal Digital Signature" xmpDM:startTime="806800" tscDM:image="l_13ds_Thumbnails.png" tscDM:imageindex="12" tscDM:imageoffset="0" tscDM:imagerect="900, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="ElGamal Digital Signatures" xmpDM:startTime="1041133" tscDM:image="l_13ds_Thumbnails.png" tscDM:imageindex="13" tscDM:imageoffset="0" tscDM:imagerect="975, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="ElGamal Digital Signature" xmpDM:startTime="1053900" tscDM:image="l_13ds_Thumbnails.png" tscDM:imageindex="14" tscDM:imageoffset="0" tscDM:imagerect="1050, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="ElGamal Signature Example " xmpDM:startTime="1083200" tscDM:image="l_13ds_Thumbnails.png" tscDM:imageindex="15" tscDM:imageoffset="0" tscDM:imagerect="1125, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="ElGamal Digital Signature" xmpDM:startTime="1184033" tscDM:image="l_13ds_Thumbnails.png" tscDM:imageindex="16" tscDM:imageoffset="0" tscDM:imagerect="1200, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="ElGamal Signature Example " xmpDM:startTime="1188833" tscDM:image="l_13ds_Thumbnails.png" tscDM:imageindex="17" tscDM:imageoffset="0" tscDM:imagerect="1275, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Schnorr Digital Signatures" xmpDM:startTime="1262333" tscDM:image="l_13ds_Thumbnails.png" tscDM:imageindex="18" tscDM:imageoffset="0" tscDM:imagerect="1350, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="ElGamal Signature Example " xmpDM:startTime="1283333" tscDM:image="l_13ds_Thumbnails.png" tscDM:imageindex="19" tscDM:imageoffset="0" tscDM:imagerect="1425, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Schnorr Digital Signatures" xmpDM:startTime="1298500" tscDM:image="l_13ds_Thumbnails.png" tscDM:imageindex="20" tscDM:imageoffset="0" tscDM:imagerect="1500, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="ElGamal Signature Example " xmpDM:startTime="1305267" tscDM:image="l_13ds_Thumbnails.png" tscDM:imageindex="21" tscDM:imageoffset="0" tscDM:imagerect="1575, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="ElGamal Digital Signature" xmpDM:startTime="1330167" tscDM:image="l_13ds_Thumbnails.png" tscDM:imageindex="22" tscDM:imageoffset="0" tscDM:imagerect="1650, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="ElGamal Signature Example " xmpDM:startTime="1355700" tscDM:image="l_13ds_Thumbnails.png" 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