Proof of 4 square roots mod pq
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...
View ArticleWEP attacks
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:...
View ArticleExtended Euclidean in Python
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...
View ArticleSquare roots mod p
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...
View ArticleLow entropy compression
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...
View ArticleZero knowledge login
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...
View ArticleQuadratic Residues in Z mod a Blum integer
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...
View ArticleEGCD
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...
View ArticleBit security for DLOG
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...
View ArticleChaum’s E-cash
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...
View Article
