Forgery Attack The attacker tries to find the signature s from a given message m and the public key message m F forgery signature s ofm lbic ke attacker (d: secret key 16
16 Forgery Attack The attacker tries to find the signature s from a given message m and the public key. Forgery attacker message m public key signature s of m (d: secret key )
Existential Forgery Attack The attacker tries to find a pair of a message and its signature from the public key (m,s): pair of public key Existential message Forgery Attacker and signature (d: secret key The message of the pair may have no meanings 17
17 Existential Forgery Attack Existential Forgery Attacker public key (m,s): pair of message and signature. The attacker tries to find a pair of a message and its signature from the public key. The message of the pair may have no meanings. (d: secret key )
Chosen Message Attack The attacker tries to find a pair(m,s) from several pairs of signature (m; Si) and the public key ms Chosen message ablie pair of message public key Attacker and signature (d: secret key messages m S(m): signatures Signing oracle If the attacker can choose new messages dependent to obtained signatures it is called the adaptive chosen message attack
18 Chosen Message Attack The attacker tries to find a pair (m,s) from several pairs of signature (mi ,si ) and the public key. Chosen Message Attacker public key (m,s): pair of message and signature. (d: secret key ) Signing Oracle messages m Sd (m): signatures If the attacker can choose new messages dependent to obtained signatures, it is called the adaptive chosen message attack
The rsa digital signature Let n= pq, where p and g are primes Let p=A=Z. and define K=i(n,p, q, e, d): ed=1 mod f(n)) For each key K=(n,p, g, e, d), define sigK(m)=ma mod n and verk(m,y)=true t ye=m mod n, where(m,y)∈ n Public key =(n, e), Private key(n, d) 19
19 The RSA digital signature Let n = pq, where p and q are primes. Let P = A = Zn , and define K = {(n,p,q,e,d) : ed = 1 mod f(n) }. For each key K = (n,p,q,e,d), define sigK(m) = md mod n and verK(m,y) = true ye = m mod n, where (m,y) Zn . Public key = (n,e), Private key (n,d).