Efficient and secure cryptographic coupon reloading

An electronic circuit for consuming cryptographic reduced-coupons containing a processor and a memory, wherein a coupon comprises, a pseudo-random number ri=PRFK(i), where i is an index for labeling the coupon, PRF is a predetermined pseudo-random function and K is a regeneration key, and a “reduced-coupon” xi such that xi=ƒ(ri), where ƒ is a predetermined one-way function, said processor and said memory being arranged to:

• acquire a value of a token T using the processor,
• receive a verification value vT,
• verify whether said verification value vT is given by vT=PRF′Q(T), where Q is an authentication key and PRF′ is a predetermined keyed pseudo-random function identical to, or derived from, said pseudo-random function PRF, and
• receive and store one or several reduced-coupons in the electronic circuit,
• wherein a number of reduced-coupons xi that are pre-stored in the electronic circuit has reached a predetermined low amount.

An Application Specific Integrated Circuit, comprising micro-components arranged to:

• acquire a value of a token T,
• receive a verification value vT,
• verify whether said verification value vT is given by vT=PRF′Q(T), where Q is an authentication key and PRF′ is a predetermined keyed pseudo-random function identical to, or derived from, said pseudo-random function PRF, said pseudo-random function being adapted to generate a pseudo-random number ri=PRFK(i), where K is a regeneration key, and i is an index for labeling a cryptographic coupon, said coupon comprising the pseudo-random number ri=PRFK(i), and, a “reduced-coupon” xi such that xi=ƒ(ri), where ƒ is a predetermined one-way function, and
• receive and store one or several reduced-coupons xi in the Application Specific Integrated Circuit,
• wherein a number of reduced-coupons xi that are pre-stored in the Application Specific Integrated Circuit has reached a predetermined low amount.

A terminal to exchange data with a portable device to provide it with reduced-coupons, wherein a coupon comprises, a pseudo-random number ri=PRFK(i), where i is an index for labeling a cryptographic coupon, PRF is a predetermined pseudo-random function, and K is a regeneration key, and a “reduced-coupon” xi such that xi=ƒ(ri), where ƒ is a predetermined one-way function, said terminal comprising a data processing device arranged to:

• acquire a value of a token T,
• generate a verification value vT is given by vT=PRF′Q(T), where PRF′ is a predetermined keyed pseudo-random function identical to, or derived from, said pseudo-random function PRF and where Q is an authentication key known to the terminal,
• transmit said verification value vT,
• generate a certain number of pseudo-random number ri,
• compute associated reduced-coupon xi, and
• transmit computed reduced-coupons to the portable device
• wherein a number of reduced-coupons xi that are pre-stored in the portable device has reached a predetermined low amount.