I'd be a noob in cryptography but reading up a little on RSA, I do get some understanding and I want to specifically resolve this issue.
Lets say we have the following values in place:
KEYSIZE = 512 HASHSIZE = sha.digestsize*8 digest = some SHA 512 function
We calculate the pub_key,pvt_key e,d via n = pq and totient function phy = (p-1)(q-1) in effect getting 1 < e < tot_func and we get d=e mod tot_func
PS : pub and pvt keys are created as an RSA_function(KEYSIZE)
Implementing an RSA scheme, we have a token m
c(m) = m^e mod n
Decrypting it would be:
m = c^d mod n
PS: m is a token number (instead of padding a m=token hash, converted from some m=f(M)) To be specific:
m = convert_str_to_long(sha_digest(M))
M itself is of random HASHSIZE bits
I want to know where I'm going wrong with this. Given the same scheme as above for token id m, However I want to be clear with a Chaum's blinding scheme and implement that instead.
we have n,p,q,d,e,m
To blind quoting from Blinding
For example, in RSA blinding involves computing the blinding operation E(x) = xr^e mod N, where r is a random integer between 1 and N and relatively prime to N (i.e. gcd(r, N) = 1), x is the ciphertext, e is the public RSA exponent and N is the RSA modulus. As usual, the decryption function f(z) = zd mod N is applied thus giving f(E(x)) = x^dr^ed mod N = x^d*r mod N. Finally it is unblinded using the function D(z) = zr^−1 mod N. Since D(f(E(x))) = x^d mod N, this is indeed an RSA decryption. However, when decrypting in this manner, an adversary who is able to measure time taken by this operation would not be able to make use of this information (by applying timing attacks RSA is known to be vulnerable to) as she does not know the constant r and hence has no knowledge of the real input fed to the RSA primitives.
Blind requires creating a blinding factor,r.
while 1: r = random.getrandbits(KEYSIZE-1) Verify that GCD(r, n) ==1 if gcd(r, n)==1: break;
- Create a blinding factor, r
- Create blinded_token = m * (r^e % n)
- What the heck do you do after that? Decrypt > Unblind Or Unblind > Decrypt to recover token m?
- Also, if you want to sign the blinded_token do you Sign > Decrypt > Unblind OR Sign > Unblind > Decrypt ?
- How do you Unblind actually based on above blinding?
My goal is to recover back m.
Please do tell me if you need some more info. I need this asap.
Thanks in advance!