{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

applied cryptography - protocols, algorithms, and source code in c

After picking x alice could break step 2 into two

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: SA prime generation, one that embeds q and the parameters used to generate the primes within p. Whether this scheme reduces the security of DSA is still unknown. (1) Choose an arbitrary sequence of at least 160 bits and call it S. Let g be the length of S in bits. (2) Compute U = SHA(S) • SHA ((S + 1) mod 2g), where SHA is the Secure Hash Algorithm (see Section 18.7). (3) Form q by setting the most significant bit and the least significant bit of U to 1. (4) Check whether q is prime. (5) Let p be the concatenation of q, S, C, and SHA(S). C is set to 32 zero bits. (6) p = p – (p mod q) + 1. (7) p = p + q. (8) If the C in p is 0x7fffffff, go to step (1). (9) Check whether p is prime. (10) If p is composite, go to step (7). The neat thing about this variant is that you don’t have to store the values of C and S used to generate p and q; they are embedded within p. For applications without a whole lot of memory, like smart cards, this can be a big deal. 20.3 GOST Digital Signature Algorithm This is a Russian digital signature standard, officially called GOST R 34.10-94 [656]. The algorithm is very similar to DSA, and uses the following parameters p = a prime number, either between 509 and 512 bits long, or between 1020 and 1024 bits long. q = a 254- to 256-bit prime factor of p – 1. a = any number less than p – 1 such that aq mod p = 1. x = a number less than q. y = ax mod p. The algorithm also makes use of a one-way hash function: H(x). The standard specifies GOST R 34.11-94 (see Section 18.11), a function based on the GOST symmetric algorithm (see Section 14.1) [657]. The first three parameters, p, q, and a, are public and can be common across a network of users. The private key is x; the public key is y. To sign a message, m (1) Alice generates a random number, k, less than q (2) Alice generates r = (ak mod p) mod q s = (xr + k(H(m))) mod q If H(m) mod q = 0, then set it equal to 1. If r = 0, then choose another k and start again. The signature is two numbers: r mod 2256...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern