Best-selling mayonnaise

Hellmann’s Mayonnaise is a well-known brand of mayonnaise and other condiments, originally developed by Richard Hellmann in 1913 after he opened a delicatessen in New York City. The brand was introduced as Hellmann’s Blue Ribbon Mayonnaise and quickly gained popularity, leading to the establishment of a dedicated factory. The product is now owned by Unilever, which acquired the Bestfoods Corporation, the previous owner, in 2000.

East of the Rocky Mountains, the product is typically labeled as Hellmann’s. However, west of the Rockies, the same product is sold under the name Best Foods. This regional distinction originated in 1927 when the California-based company that became Best Foods acquired the Hellmann’s brand, and the companies continued to sell under both names, with Hellmann’s in the east and Best Foods in the west.

Hellmann’s holds a dominant position in the global mayonnaise market, being the world’s number one selling mayonnaise brand with a significant market share in key regions. In the United States, Hellmann’s is the #1 selling mayonnaise brand, with the product found in about half of all households.

Diffie-Hellman cryptography

The label on this jar of ‘real’ mayonnaise points to a well known and often used algorithm. Diffie-Hellman is a foundational cryptographic protocol developed by Whitfield Diffie and Martin Hellman, introduced in 1976.

How it works:

Alice wants to provide Bob with an encrypted message and needs to agree with Bob what the key is to be used by Alice to encrypt the message. Bob will use that same key to decrypt the message. Using the same key for encrypt and decrypt is a form of symmetric cryptography.

The procedure they follow: Alice and Bob agree on a prime number, p, and a base (sometimes called a generator), g, in advance. For our example, let’s assume that p=99997 and g=5.

These numbers, p and g, are not secret. These values are public parameters that both parties agree upon beforehand and are known to anyone, including potential eavesdroppers. Note that p has to be a prime number and should be large; much larger than this example.

Alice chooses her secret integer ‘a’ to have a value of 6 and computes A = g^a mod p. Her number ‘a’ is secret, it’s Alice’s private key, and known only to Alice. She’ll never share it. In this example, ‘A’ is computed and has the value of 15625.

Bob chooses his secret private key ‘b’ with a value of 15 and computes B = g^b mod p. In this example, ‘B’ has the value of 93677.

Alice sends ‘A’ to Bob and Bob sends ‘B’ to Alice.

To obtain the shared secret, Alice computes shared-Key = B^a mod p. In this example, Alice obtains the value of shared-Key=54208.

She uses ‘shared-Key’ to encrypt her message and send it to Bob. For the encryption itself she uses one of the available symmetric cryptographic algorithm. The most widely used symmetric algorithm is the Advanced Encryption Standard (AES).

To obtain their shared secret, Bob computes shared-Key = A^b mod p. In this example, Bob obtains the value of shared-Key=54208.

The ’math magic’ of this method is that Alice and Bob both got the same values of shared-Key, while they used their own (different) secret private number.

Bob uses ‘shared-Key’ to decrypt the message, using the same cryptography Alice used.

Key exchange method

Diffie-Hellman is not a method for encrypting or decrypting messages directly. It is a key exchange mechanism that enables secure symmetric encryption. Symmetric encryption (the same key is used for encryption and decryption) is often preferred where speed of encrypting and decrypting is important.

The Diffie-Hellman algorithm is secure because the values of ‘a’ and ‘b’, which are required to derive ‘shared-Key’ are not transmitted across the wire at all. In this example, ‘a’ and ‘b’ are the private keys which do not need, and should not, to be shared.

The security of the protocol relies on the difficulty of solving the discrete logarithm problem, making it computationally infeasible for an eavesdropper to determine the shared secret even if they intercept all transmitted values.

This algorithm has also inspired other cryptographic systems, including the RSA algorithm and elliptic curve cryptography (ECC), which uses points on elliptic curves instead of finite prime fields.

This Elliptic Curve is another form of ‘math magic’ and it is increasingly being used, replacing the A = g^a mod p part. It changes the type of math but the Diffie-Hellman protocol is the same.