CSci 5471: Modern Cryptography
Homework 5
due: May 1, 2013
Ground Rules. You may choose to complete these homeworks in a group of up to three students.
Each group should turn in one copy with the names of all group members on it. You may use any
source yo

Modern Cryptography
CSCI 5471, Spring 2013
Bob publishes public (encryption) key pk
keeps secret secret (decryption) key sk
Bob
Alice
PK
E(PK,m)
E(pk,m)
Man in the middle attacks: How does Alice know PK?
CERTIFICATES
Digitally signed:
Encryption PK
Sig

Modern Cryptography
CSCI 5471, Spring 2013
SECRET SHARING
Dealer has secret x q.
Shareholders S1Sn get shares s1sn.
Access Structure : a set of subsets A1
Am, Ai cfw_1n.
Security property: for any B cfw_1n,
If B , then Reconstruct(cfw_si | i B) = x

Modern Cryptography
CSCI 5471, Spring 2013
MULTIPLICATION MOD M
Definition. Let a . a* is the arithmetic inverse
of a modulo m, if aa* a*a 1 (mod m).
Theorem. a-1 (mod m) exists iff gcd(a,m)=1.
aa* = km+1 a(a*) m(k) = 1 gcd(a,m)=1
gcd(a,m)=1 x,y ax+my =

Modern Cryptography
CSCI 5471, Spring 2013
BLIND SIGNATURES
KeyGen(1k): VK, SK
Blind(VK,m): ,
Sign(SK, ):
Unblind(,):
Verify(PK, m, ): T/F
CHAUM BLIND SIGNATURES
Alice
VK = (N,e)
Bob
= re h(m) mod N
= d mod N
= r -1 mod N
is an RSA-FDH signature on

Modern Cryptography
CSCI 5471, Spring 2013
IDENTITY-BASED ENCRYPTION
Publishes
MPK
Alice
Im Bob!
SKBob
Bob
E(Bob,m)
Formally, four algorithms:
Setup(1k): Generates (MPK, MSK)
Extract(MSK,ID): Computes SKID.
Encrypt(MPK,ID,m): encrypts m for ID.
Decrypt(SK

CSci 5471: Modern Cryptography
Homework 1
due: February 6, 2013
Ground Rules. You may choose to complete these homeworks in a group of up to three students.
Each group should turn in one copy with the names of all group members on it. You may use any
sour

CSci 5471: Modern Cryptography
Homework 4
due: April 17, 2013
Ground Rules. You may choose to complete these homeworks in a group of up to three students.
Each group should turn in one copy with the names of all group members on it. You may use any
source

CSci 5471: Modern Cryptography
Homework 3
due: March 15, 2013
Ground Rules. You may choose to complete these homeworks in a group of up to three students.
Each group should turn in one copy with the names of all group members on it. You may use any
source

CSci 5471: Modern Cryptography
Homework 2
due: February 25, 2013
Ground Rules. You may choose to complete these homeworks in a group of up to three students.
Each group should turn in one copy with the names of all group members on it. You may use any
sou