You are welcome to use Maple, Mathematica, or MATLAB to work out
these problems. However, you need to show how you computed the
final values and also show some intermediate values
obtained from your calculations. In other words, I need some
proof that it was actually you that was computing.
- Let an RSA public key system be determined by the parameters
- (e,n)=(37,2953401912753470184385527395089)
Given the following two messages and their signatures
- (M1,S1)=(123456787654321,2529045382792077409201907200017)
- (M2,S2)=(876543212345678,1783412625941219914738123477721)
obtain signatures for the following messages by applying forging:
- M3=108215209236396770461822374638
- M4=2289000134448567813784851259005
- M5=1970129874192430866971371299001
- M6=1440262305070617466187763812276
Hint: The multiplicative property of the RSA algorithm needs
to be used. You are not supposed to factor n and find p, q,
and d, and therefore, break the RSA system. The multiplicative
properties of the RSA signature are as follows:
Sign(x*y)=Sign(x)*Sign(y)
Sign(x^{-1})=Sign(x)^{-1}
- Let a DSS system be determined by the parameters p=15444934501,
q=130337. A primitive element mod p is given as g=11. Compute
alpha: the primitive qth root of 1 modulo p. Let the private key be
d=29290. Compute y (the public key). Obtain the signature on the
message H(m)=27022004 with the random value k=1502980. Also show the
verification steps.
- Let a ECDSA over GF(p) system be determined by the elliptic
curve group a=1, b=4, p=19, that is the elliptic curve equation is
y^2 = x^3 + x + 4 over GF(19). Do the following:
- List all points on this curve
- Find the order of the group
- Select the basis point P=(5,1) and find the order of P
- Is the order of P equal to the order of group? Why?
- Give another point on the curve with the same order.
After finding n (order of the elliptic curve group and the order
of the basis point P), take the private key as d=7 and compute the
following:
- Compute the public key Q=(x,y)
- Obtain the signature (r,s) on the message H(m)=9
with the random value k=5
- Show the verification steps.
- This is a question about AES. Given the plaintext
000102030405060708090A0B0C0D0E0F (hex)
and the key
01010101010101010101010101010101 (hex)
- Compute the original contents of State, displayed as a 4x4 matrix.
- Compute the value of State after initial AddRoundKey.
- Compute the value of State after SubBytes.
- Compute the value of State after ShiftRows.
- Compute the value of State after MixColumns.
- This is a question about AES. Compute the first and second 4x4
round key matrices w[0,3] and w[4,7] produced by the key expansion
procedure when the 128-bit key is all 1s.
Email me the Word, PDF, or text file.
My email address is koc@ece.orst.edu.
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