'crypto' Category

  • Chaum’s E-cash

    April 21, 2014

    This follow the exposition by Mira Belenkiy in The Handbook of Financial Cryptography, edited by Burton Rosenberg. E-cash is one of many forms of financial instruments, an alternative to cash. Cash itself isn’t well understood. There are those that think of cash as an easy form of gold transfer, called the gold standard, and those [...]

  • Bit security for DLOG

    April 5, 2014

    The DLOG assumption is that given a prime p, and a generator α of the group of units mod p, <α>=Zpx, that the map αi → i is not polynomial-time computable. However it is not true that every bit of information about i is unattainable. Most notably, the parity of i is easily determined. If [...]

  • EGCD

    January 22, 2014

    The best way I think to understand the Euclidean Greatest Common Divisor algorithm is to think big. For the GCD of two numbers, a and b, rather than think about the few numbers, a, b, a%b, b%(a%b), and so forth, think about all numbers of the form i*a+j*b. Note that a%b = i*a+j*b, for some [...]

  • Quadratic Residues in Z mod a Blum integer

    April 23, 2012

    Blum integers are integers n such that n is the product of two distinct primes p and q, where p and q are both 3 mod 4. The permutation given by x goes to x squared mod n, when restricted to the quadratic residues of the integers mod n, is the basis of the Blum-Blum-Shub [...]

  • Zero knowledge login

    April 16, 2012

    Some authentication mechanisms depend on a secret knowledge to identify the subject. For instance, knowledge of a password. To prove knowledge of the password, the subject produces the password. This requires that the authenticating party know the password as well, so the knowledge is not that secret. The authenticating party must be authenticated, else that [...]

  • Low entropy compression

    March 22, 2012

    Huffman coding doesn’t seem to do the right thing in cases of low entropy, such as a 0-1 data source where p, the probability of a zero, is very close to 1. One possibility is to batch several symbols into one, block encoding, and Huffman code over the blocks. Letting block size increase should limit [...]

  • Square roots mod p

    April 12, 2010

    The structure of Z/pZ (a.k.a. integers mod p) is simple when p-1 is not divisible by 4, that is, p=3 (4). In this case -1 is a quadratic non-residue, else there would be a subgroup of the four 4-th roots of 1, and the order of a subgroup divides the order of the group. Therefore [...]

  • Extended Euclidean in Python

    April 12, 2010

    This from Active state def egcd(a,b): # a > b > 0 ___”"” Extended great common divisor, returns x , y and gcd(a,b) so ax + by = gcd(a,b) “”" ___if a%b==0: ______return (0,1,b) ___q=[] ___while a%b != 0: ______q.append(-1*(a//b)) ______(a,b)=(b,a%b) ___(a,b,gcd)=(1,q.pop(),b) ___while q: ______(a,b)=(b,b*q.pop()+a) ___return (a,b,gcd) For information about Idle on the PC and [...]

  • WEP attacks

    March 18, 2010

    History of WEP cracks, starting with Wagner, leading to KoreK, including FMS like weak keys and chopchop, which really works on any single byte without chopping: http://www.netstumbler.org/showthread.php?t=12277 A description of some of the extensions to FMS: http://www.netstumbler.org/showpost.php?p=89036&postcount=11 I think there is also notations inside the code. This is copied from an older wiki entry.

  • Proof of 4 square roots mod pq

    March 18, 2010

    Square the relation sq+rp=1. Mod pq inner terms cancel, and outer terms are invariant to signs of s and r. So the four square roots of unity mod pq are (+/-)(sq+rp) and (+/-)(sq-rp). This article is brought forward from a wiki page dated 2006/05/18 11:43.

 
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