def generateAuxInfo(s, prime):
"""Generates auxilliary information for a msg integer s to satisfy the
quation c = bs + y where b and y are randomly generated numbers. Each
of c, b and y are values module prime.
Args:
s: A integer message for which the auxilliary information is to be
generated.
prime: A integer value specifying the prime field for modulo operations.
Returns:
A list consisting of values [c, b, y] that satisfies the equation
c = bs + y.
Raises:
TypeError: Error when either the s or prime is not a integer.
ValueError: Error when prime is not greater than the given value of s.
"""
if type(s) not in [int, long]:
raise TypeError("invalid msg: int or long expected")
elif type(prime) not in [int, long]:
raise TypeError("invalid prime: int or long expected")
elif s >= prime:
raise ValueError("invalid prime: value larger than s expected")
b = genRandNum(prime)
y = genRandNum(prime)
c = (b * s + y) % prime
return [c, b, y]
def randomPolynomial(k, prime):
"""Generates a random polynomial y = msgNum + c[0]*x + c[1]*x^2 + ...
+ c[k-2]*x^(k-1) by generating the list of cryptographically secure
coefficients c[i] using prime as the order of modulo operations.
Args:
k: An integer value representing the number of coefficients to be
generated.
prime: An integer value to be used as the order of modulo operations.
Returns:
A list of k-1 randomly generated coefficients for the polynomial
y = msgNum + c[0]*x + c[1]*x^2 + ... + c[k-2]*x^(k-1)
Raises:
TypeError: Error when either k or prime is not an integer.
"""
if type(k) not in [int, long]:
raise TypeError("invalid k: int or long expected")
elif type(prime) not in [int, long]:
raise TypeError("invalid prime: int or long expected")
coefficients = []
for i in range(1, k):
coefficients.append(genRandNum(prime))
return coefficients
