Strong cryptography is secreted and encrypted communication that is well-protected against cryptographic analysis and decryption to ensure it is readable only to intended parties.
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Depending on the algorithms, protocols and implementation, a cryptographic system may be vulnerable to analysis, leading to possible cracking of the system. The ideal is an unbreakable system of which there is just one well known example: the one-time pad. The one-time pad is a system in which a randomly generated single-use private key is used to encrypt a message. The message is then decrypted by the receiver using a matching one-time pad and key. The challenge in this system is exchanging pads and keys without allowing them to be compromised.
Strong cryptography is used by most governments to protect communications. While it is increasingly available to the general public, there are still many countries where strong cryptography and encryption are kept from the general public, justified by the need to protect national security.
While the definition of strong cryptography in general may be broad, the The PCI Security Standards Council defines strong cryptography requirements for use in the payment card industry (PCI) specifically:
“Cryptography based on industry-tested and accepted algorithms, along with strong key lengths (minimum 112-bits of effective key strength) and proper key-management practices. Cryptography is a method to protect data and includes both encryption (which is reversible) and hashing (which is not reversible, or “one way”). At the time of publication, examples of industry-tested and accepted standards and algorithms for minimum encryption strength include AES (128 bits and higher), TDES (minimum triple-length keys), RSA (2048 bits and higher), ECC (160 bits and higher), and ElGamal (2048 bits and higher).”
Demonstrating the strength of a given cryptographic system is a complex affair that requires in-depth consideration. As such, the demonstration is best achieved by a large number of collaborators. Planning tests, sharing and analyzing and reviewing of results are best conducted in a public forum.