Cryptographic Data Objects B has just received the following message, which represents a cryptographic data object: {( {(KPbB) KPrS mod KPbS}K1, {|(NB, NA, {{({K2}KPbB, NS)}(G1) KPrA mod NA}K1, {|{({G3}(KPbA) KPrS mod KPbS, G2)}K1|}KPrB)|}KPrA )}KBS The following explains various terms in this object and some of the abbreviations used: • {M}K represents the encryption of some message/data M using the key K • {|M|}K represents the digital signing of some message/data M using the key K • NX represents a nonce (i.e. a fresh and possibly random number used once only) generated by X • KpbX represents the public part of the key pair presumably owned by X • KprX represents the private part of the key pair presumably owned by X • KAB represents a symmetric key shared between A and B • K (or K1, K2, K3 etc.) represents some arbitrary key with no assumptions about its scope • M represents some alphanumeric/textual message with no assumptions • G1, G2, G3 etc. are prime numbers Which of the following sets of keys, nonces, numbers, and alphanumeric/textual messages “best” represents B’s knowledge, after B applies any number of possible cryptographic operations to the object above, and assuming that B already has access to key K1 and the public key of any agent: a) KBS , G2 , KPrB b) {(KPbB) KPrS mod KPbS , G2 , KBS , KPrB , {(KPbB) KPrS mod KPbS}K1, NA , NB c) NA , NB d) NA , NB , KBS , KPrB e) {(KPbB) KPrS mod KPbS}K1 , {|(NB, NA, {{({K2}KPbB, NS)}(G1) KPrA mod NA}K1, {|{({G3}(KPbA) KPrS mod KPbS, G2)}K1|}KPrB)|}KPrA , NA , NB , KBS , KPrB , {(KPbB) KPrS mod KPbS f) G2 , NA , NB , G1 , KBS , KPrB g) (KPbB) KPrS mod KPbS , NA , NB , G2 , KBS , KPrB h) (KPbB) KPrS mod KPbS , (G1) KPrA mod NA , NA, NB , G2 , KBS , KPrB i) (KPbB) KPrS mod KPbS , G3 , G2 , KBS , KPrB j) (KPbB) KPrS mod KPbS , NA , NB , G2 , KBS , KPrB , G3 , (KPbA) KPrS mod KPbS k) NB Explain your answer below
Cryptographic Data Objects
B has just received the following message, which represents a cryptographic data object:
{(
{(KPbB)
KPrS mod KPbS}K1,
{|(NB, NA, {{({K2}KPbB, NS)}(G1)
KPrA mod NA}K1, {|{({G3}(KPbA)
KPrS mod KPbS, G2)}K1|}KPrB)|}KPrA
)}KBS
The following explains various terms in this object and some of the abbreviations used:
• {M}K represents the encryption of some message/data M using the key K
• {|M|}K represents the digital signing of some message/data M using the key K
• NX represents a nonce (i.e. a fresh and possibly random number used once only) generated
by X
• KpbX represents the public part of the key pair presumably owned by X
• KprX represents the private part of the key pair presumably owned by X
• KAB represents a symmetric key shared between A and B
• K (or K1, K2, K3 etc.) represents some arbitrary key with no assumptions about its scope
• M represents some alphanumeric/textual message with no assumptions
• G1, G2, G3 etc. are prime numbers
Which of the following sets of keys, nonces, numbers, and alphanumeric/textual messages “best”
represents B’s knowledge, after B applies any number of possible cryptographic operations to the
object above, and assuming that B already has access to key K1 and the public key of any agent:
a) KBS , G2 , KPrB
b) {(KPbB)
KPrS mod KPbS , G2 , KBS , KPrB , {(KPbB)
KPrS mod KPbS}K1, NA , NB
c) NA , NB
d) NA , NB , KBS , KPrB
e) {(KPbB)
KPrS mod KPbS}K1 , {|(NB, NA, {{({K2}KPbB, NS)}(G1)
KPrA mod NA}K1, {|{({G3}(KPbA)
KPrS mod
KPbS, G2)}K1|}KPrB)|}KPrA , NA , NB , KBS , KPrB , {(KPbB)
KPrS mod KPbS
f) G2 , NA , NB , G1 , KBS , KPrB
g) (KPbB)
KPrS mod KPbS , NA , NB , G2 , KBS , KPrB
h) (KPbB)
KPrS mod KPbS , (G1)
KPrA mod NA , NA, NB , G2 , KBS , KPrB
i) (KPbB)
KPrS mod KPbS , G3 , G2 , KBS , KPrB
j) (KPbB)
KPrS mod KPbS , NA , NB , G2 , KBS , KPrB , G3 , (KPbA)
KPrS mod KPbS
k) NB
Explain your answer below
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