To answer the OP direct question this is my understanding by reading the spec and API docs. Everything is closed source and some low level details are simply not provided so assumptions and inferences which may later prove to be incorrect had to be made.
How it works?
The blockchain is the cornerstone technology for Bitcoin. Without the blockchain nothing is possible. The equivelent in MintChip system is the physical MintChip ("the chip"). The chip is a physically hardened tamper resistant cryptographic processor. It will be available in a variety of formats (SD card, USB stick, crypto module) but the internal chip is the same.
The chip has four key functions:
a) protects a private key from extraction (and provide access to the corresponding public key).
b) sign outgoing tx w/ private key
c) verify incoming tx as valid
d) process tx to update an internal record of current balance and enforce rules based on that internal balance value (i.e. can't spend money you don't have).
Like in Bitcoin the private key "controls" the funds but unlike in Bitcoin the private key is kept private
even from the user. The private key is known only to the chip.
The entire security model works around the inability for anyone even the owner/user to ever know the private key.There is no central ledger (either private like in Paypal or distributed like in Bitcoin). Duplicate tx (double spends) in Bitcoin can be easily made as the user has access to private key. To prevent that Bitcoin uses the distributed consensus created by the blockchain and forwarding rules by nodes to make double spend attempts "easy but uneconomical".
With no central ledger each chip uses the public key of the sending chip, the signature or the tx, and a nonce to ensure that tx can't be faked. If the tx is valid then the chip assumes it had to have been created by the sender's chip. Given the private key is known only to the chip normally that is a valid assumption. If someone could extract the private key from the chip they could fake txs at will. Essentially print money from nothing.
For the system work nobody can ever extract the private key from any MintChip under any circumstances until the end of time. Given the track record of "secret of a chip" systems it is an inevitability that someone will eventually be able to extract a private key and "counterfeit" funds. Unlike physical counterfeiting there would be no incremental cost and counterfeit txs would be indistinguishable from valid txs.
Much like 51% attack is the Achilles heel of Bitcoin the extraction of private key from "the chip" is the Achilles heel of MintChip.The "nobody not even user can know the secret key" limitation of MintChip creates some unique non-counterfeiting limitations:
a) deterministic wallets are impossible. your chip is the wallet there is no exceptions.
b) backups of funds are impossible. funds on lost/damaged chips are lost forever.
c) impossible to make "strongcoin" like limited trust ewallet services. An ewallet provide will need physical access to "your chip" and thus 100% implicit trust is required.
d) unlike in Bitcoin double spends can't be detected. Thus if fraud occurs the funds in circulation will be larger than the reserves held. How this will be handled is unknown (central bank prints to cover the increase? fees remove funds from circulation? exchange rate between physical CAD : mintchip CAD drops below 1:1?)