The discrete logarithm problem (DLP) is one of the cornerstones of the fields of cryptology and cryptography. It is described using a finite cyclic group G with a generator g (primitive root modulo p); an element h, where h is an element in the group G and generated by g; and a prim...
Cryptography Classical cryptography—such as the Rivest–Shamir–Adleman (RSA) algorithm that’s widely used to secure data transmission—relies on the intractability of problems such as integer factorization or discrete logarithms. Many of these problems can be solved more efficiently using quantum com...
That makes lattice-based problems good replacements for prime factorization problems in cryptography. A short window to prepare The good news is that quantum-safe cryptography already exists. We are so confident in these new standards that we have already built them into IBM z16™ cloud ...
RSA is one of the oldest public-key cryptography systems. It's a type of asymmetric or "public key" encryption that, like ECC, uses two private and public keys. Either key can be used to encrypt a message, while the other key is used to decrypt it. The security of the RSA algorithm...
Shor’s algorithm for integer factorization demonstrated how a quantum mechanical computer could potentially break the most advanced cryptography systems of the time—some of which are still used today. Shor’s findings demonstrated a viable application for quantum systems, with dramatic implications for...
This is a review of the issue of randomness in quantum mechanics, with special emphasis on its ambiguity; for example, randomness has different antipodal relationships to determinism, computability, and compressibility. Following a (Wittgensteinian) philosophical discussion of randomness in general, I ar...
and their work, let’s look at how they’re used in cryptography. Elliptic curve cryptography typically relies on theElliptic Curve Discrete Logarithm Problem (ECDLP), which states that it is hard to solve for x if we know y = g^x mod p where g is some known integer and p is prime...
What is a prime number? Cryptography: In order to create secure keys for cryptography, the knowledge of prime numbers is essential. Despite being infinite, they become less frequent as numbers increase, making it difficult to identify huge primes and stressing their importance in both theoretical ...
Whitfield Diffie, a researcher at Stanford, andMartin Hellman, a professor at Stanford, began collaborating to address this problem during the early 1970s. In 1976, the two introduced the concept of public-key cryptography in a paper titled "New Directions in Cryptography." ...
Asymmetrical cryptography is used in a lot of different places, not just in internet funnymoney. Speaking of which, there’s one more technology we need to understand to make sense of this Bitcoin stuff: Hash Functions Information in, garbage out. I don't see what the big deal is. A lot...